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College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista, Betty McCarthy Richardson , Robert C. Richardson

Chapter 4

Motion with Constant Acceleration - all with Video Answers

Educators

Chapter Questions

02:08

Problem 1

An airplane lands and starts down the runway at a southwest velocity of $55 \mathrm{~m} / \mathrm{s}$. What constant acceleration allows it to come to a stop in $1.0 \mathrm{~km}$ ?

Wesley Hines
Wesley Hines
Numerade Educator
02:22

Problem 2

A car is speeding up and has an instantaneous velocity of $1.0 \mathrm{~m} / \mathrm{s}$ in the $+x$ -direction when a stopwatch reads $10.0 \mathrm{~s}$. It has a constant acceleration of $2.0 \mathrm{~m} / \mathrm{s}^{2}$ in the $+x$ -direction. (a) What change in speed occurs between $t=10.0 \mathrm{~s}$ and $t=12.0 \mathrm{~s} ?$ (b) What is the speed when the stopwatch reads $12.0 \mathrm{~s}$ ?

Bryce Samwel
Bryce Samwel
Numerade Educator
02:13

Problem 3

While passing a slower car on the highway, you accelerate uniformly from $17.4 \mathrm{~m} / \mathrm{s}$ to $27.3 \mathrm{~m} / \mathrm{s}$ in a time of $10.0 \mathrm{~s}$.
(a) How far do you travel during this time?
(b) What is your acceleration magnitude?

Sachin Rao
Sachin Rao
Numerade Educator
02:43

Problem 4

In a game of shuffleboard, a disk with an initial speed of $3.2 \mathrm{~m} / \mathrm{s}$ travels $6.0 \mathrm{~m}$ before coming to rest. (a) What was the magnitude of the average acceleration of the disk? (b) What was the coefficient of kinetic friction acting on the disk?

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
05:58

Problem 5

A skier with a mass of $63 \mathrm{~kg}$ starts from rest and skis down an icy (frictionless) slope that has a length of $50 \mathrm{~m}$ at an angle of $32^{\circ}$ with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of $140 \mathrm{~m}$ along the horizontal path. (a) What is the speed of the skier at the bottom of the slope? (b) What is the coefficient of kinetic friction between the skier and the horizontal surface?

Averell Hause
Averell Hause
Carnegie Mellon University
04:02

Problem 6

A cheetah can accelerate from rest to $24 \mathrm{~m} / \mathrm{s}$ in $2.0 \mathrm{~s}$. Assuming the acceleration is constant over the time interval, (a) what is the magnitude of the acceleration of the cheetah? (b) What is the distance traveled by the cheetah in these $2.0 \mathrm{~s}$ ? (c) A runner can accelerate from rest to $6.0 \mathrm{~m} / \mathrm{s}$ in the same time, $2.0 \mathrm{~s}$. What is the magnitude of the acceleration of the runner? By what factor is the cheetah's average acceleration magnitude greater than that of the runner?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
03:31

Problem 7

The forces on a small airplane (mass $1160 \mathrm{~kg}$ ) in horizontal flight heading eastward are as follows: gravity $=16.000 \mathrm{kN}$ downward, lift $=16.000 \mathrm{kN}$ upward, thrust $=1.800 \mathrm{kN}$ eastward, and drag $=1.400 \mathrm{kN}$ westward. At $t=0$, the plane's speed is $60.0 \mathrm{~m} / \mathrm{s}$. If the forces remain constant, how far does the plane travel in the next $60.0 \mathrm{~s}$ ?

Averell Hause
Averell Hause
Carnegie Mellon University
03:46

Problem 8

A train of mass $55,200 \mathrm{~kg}$ is traveling along a straight, level track at $26.8 \mathrm{~m} / \mathrm{s}(60.0 \mathrm{mi} / \mathrm{h})$. Suddenly the engineer sees a truck stalled on the tracks $184 \mathrm{~m}$ ahead. If the maximum possible braking force has magnitude $84.0 \mathrm{kN}$, can the train be stopped in time?

Bryce Samwel
Bryce Samwel
Numerade Educator
02:59

Problem 9

You are driving your car along a country road at a speed of $27.0 \mathrm{~m} / \mathrm{s}$. As you come over the crest of a hill, you notice a farm tractor $25.0 \mathrm{~m}$ ahead of you on the road, moving in the same direction as you at a speed of $10.0 \mathrm{~m} / \mathrm{s}$. You immediately slam on your brakes and slow down with a constant acceleration of magnitude $7.00 \mathrm{~m} / \mathrm{s}^{2}$. Will you hit the tractor before you stop? How far will you travel before you stop or collide with the tractor? If you stop, how far is the tractor in front of you when you finally stop?

Wesley Hines
Wesley Hines
Numerade Educator
02:30

Problem 10

In a cathode ray tube, electrons are accelerated from rest by a constant electric force of magnitude $6.4 \times 10^{-17} \mathrm{~N}$ during the first $2.0 \mathrm{~cm}$ of the tube's length; then they move at essentially constant velocity another $45 \mathrm{~cm}$ before hitting the screen. (a) Find the speed of the electrons when they hit the screen. (b) How long does it take them to travel the length of the tube?

Mayukh Banik
Mayukh Banik
Numerade Educator
07:16

Problem 11

A $10.0-\mathrm{kg}$ watermelon and a $7.00-\mathrm{kg}$ pumpkin are attached to each other via a cord that wraps over a pulley, as shown. Friction
is negligible everywhere in this system. ( W tutorial:
pulley) (a) Find the accelerations of the pumpkin and the watermelon. Specify magnitude and direction. (b) If the system is released from rest, how far along the incline will the pumpkin travel in $0.30 \mathrm{~s}$ ? (c) What is the speed of the watermelon after

Vishal Gupta
Vishal Gupta
Numerade Educator
02:39

Problem 12

Two blocks are connected by a lightweight, flexible cord that passes over a frictionless pulley. If $m_{1}=3.6 \mathrm{~kg}$ and $m_{2}=9.2 \mathrm{~kg}$, and block 2 is initially at rest $140 \mathrm{~cm}$ above the floor, how long does it take block 2 to reach the floor?
While an elevator of mass $832 \mathrm{~kg}$ moves downward, the tension in the supporting cable is a constant $7730 \mathrm{~N}$.
Between $t=0$ and $t=4.00 \mathrm{~s}$, the elevator's displacement is $5.00 \mathrm{~m}$ downward. What is the elevator's speed at $t=4.00 \mathrm{~s} ?$

Averell Hause
Averell Hause
Carnegie Mellon University
03:19

Problem 13

While an elevator of mass $832 \mathrm{~kg}$ moves downward, the tension in the supporting cable is a constant $7730 \mathrm{~N}$. Between $t=0$ and $t=4.00 \mathrm{~s}$, the elevator's displacement is $5.00 \mathrm{~m}$ downward. What is the elevator's speed at $t=4.00 \mathrm{~s} ?$

Averell Hause
Averell Hause
Carnegie Mellon University
02:37

Problem 14

The graph is of $v_{x}$ versus $t$ for an object moving along the $x$ -axis. How far does the object move between $t=9.0 \mathrm{~s}$ and $t=13.0 \mathrm{~s}$ ? Solve using two methods: a graphical analysis and an algebraic solution.

Bryce Samwel
Bryce Samwel
Numerade Educator
03:17

Problem 15

The graph is of $v_{x}$ versus $t$ for an object moving along the $x$ -axis. What is the average acceleration between $t=5.0 \mathrm{~s}$ and $t=9.0 \mathrm{~s}$ ? Solve using two methods: a graphical analysis and an algebraic solution.

Shelby Mohamed
Shelby Mohamed
Numerade Educator
05:58

Problem 16

A train, traveling at a constant speed of $22 \mathrm{~m} / \mathrm{s}$, comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude $1.4 \mathrm{~m} / \mathrm{s}^{2}$. (a) Draw a graph of $v_{x}$ versus $t$ where the $x$ -axis points up the incline. (b) What is the speed of the train after $8.0 \mathrm{~s}$ on the incline? (c) How far has the train traveled up the incline after $8.0 \mathrm{~s}$ ? (d) Draw a motion diagram, showing the train's position at $2.0-\mathrm{s}$ intervals.

Shelby Mohamed
Shelby Mohamed
Numerade Educator
07:03

Problem 17

The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of $1.20 \mathrm{~m} / \mathrm{s}^{2}$ for $12.0 \mathrm{~s}$. (a) Draw a graph of $v_{x}$ versus $t .$ (b) How far has the train traveled at the end of the $12.0 \mathrm{~s}$ ? (c) What is the speed of the train at the end of the $12.0 \mathrm{~s}$ ? (d) Draw a motion diagram, showing the trolley car's position at 2.0-s interyals.

Shelby Mohamed
Shelby Mohamed
Numerade Educator
04:52

Problem 18

A streetcar named Desire travels between two stations $0.60 \mathrm{~km}$ apart. Leaving the first station, it accelerates for $10.0 \mathrm{~s}$ at $1.0 \mathrm{~m} / \mathrm{s}^{2}$ and then travels at a constant speed until it is near the second station, when it brakes at $2.0 \mathrm{~m} / \mathrm{s}^{2}$ in order to stop at the station. How long did this trip take? [Hint: What's the average velocity?]

Supratim Pal
Supratim Pal
Numerade Educator
02:48

Problem 19

In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of $25.0 \mathrm{~cm} / \mathrm{s}$ in traveling $50.0 \mathrm{~cm}$ from the starting point, what was the angle of inclination of the track? Draw a graph of $v_{x}(t)$ when the positive $x$ -axis points down the track.

Averell Hause
Averell Hause
Carnegie Mellon University
04:11

Problem 20

A $10.0$ -kg block is released from rest on a frictionless track inclined at an angle of $55^{\circ}$. (a) What is the net force on the block after it is released? (b) What is the acceleration of the block? (c) If the block is released from rest, how long will it take for the block to attain a speed of $10.0 \mathrm{~m} / \mathrm{s} ?$ (d) Draw a motion diagram for the block.
(e) Draw a graph of $v_{x}(t)$ for values of velocity between 0 and $10 \mathrm{~m} / \mathrm{s}$. Let the positive $x$ -axis point down the track.

Averell Hause
Averell Hause
Carnegie Mellon University
04:15

Problem 21

A $6.0-\mathrm{kg}$ block, starting from rest, slides down a frictionless incline of length $2.0 \mathrm{~m}$. When it arrives at the bottom of the incline, its speed is $v_{\mathrm{f}}$. At what distance from the top of the incline is the speed of the block $0.50 v_{r}$ ?

Averell Hause
Averell Hause
Carnegie Mellon University
06:46

Problem 22

A train is traveling south at $24.0 \mathrm{~m} / \mathrm{s}$ when the brakes are applied. It slows down with a constant acceleration
to a speed of $6.00 \mathrm{~m} / \mathrm{s}$ in a time of $9.00 \mathrm{~s}$. (a) Draw a graph of $v_{x}$ versus $t$ for a 12 -s interval (starting 2 s before the brakes are applied and ending 1 s after the brakes are released). Let the $x$ -axis point to the north.
(b) What is the acceleration of the train during the 9.00-s interval? (c) How far does the train travel during the $9.00 \mathrm{~s}$ ?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
02:49

Problem 23

Grant Hill jumps $1.3 \mathrm{~m}$ straight up into the air to slamdunk a basketball into the net. With what speed did he leave the floor?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
01:27

Problem 24

A penny is dropped from the observation deck of the Empire State building ( $369 \mathrm{~m}$ above ground). With what velocity does it strike the ground? Ignore air resistance.

Anand Jangid
Anand Jangid
Numerade Educator
01:55

Problem 25

(a) How long does it take for a golf ball to fall from rest for a distance of $12.0 \mathrm{~m} ?$ (b) How far would the ball fall in twice that time?

Sachin Rao
Sachin Rao
Numerade Educator
04:15

Problem 26

A student, looking toward his fourth-floor dormitory window, sees a flowerpot with nasturtiums (originally on a window sill above) pass his $2.0-\mathrm{m}$ high window in $0.093 \mathrm{~s}$. The distance between floors in the dormitory is $4.0 \mathrm{~m}$. From a window on which floor did the flowerpot fall?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
01:39

Problem 27

A balloonist, riding in the basket of a hot air balloon that is rising vertically with a constant velocity of $10.0 \mathrm{~m} / \mathrm{s}$, releases a sandbag when the balloon is $40.8 \mathrm{~m}$ above the ground. Ignoring air resistance, what is the bag's speed when it hits the ground?

Sachin Rao
Sachin Rao
Numerade Educator
02:03

Problem 28

A $55-\mathrm{kg}$ lead ball is dropped from the leaning tower of Pisa. The tower is $55 \mathrm{~m}$ high. (a) How far does the ball fall in the first $3.0 \mathrm{~s}$ of flight? (b) What is the speed of the ball after it has traveled $2.5 \mathrm{~m}$ downward? (c) What is the speed of the ball $3.0 \mathrm{~s}$ after it is released?

Sachin Rao
Sachin Rao
Numerade Educator
04:11

Problem 29

Superman is standing $120 \mathrm{~m}$ horizontally away from Lois Lane. A villain drops a rock from $4.0 \mathrm{~m}$ directly above Lois. (a) If Superman is to intervene and catch the rock just before it hits Lois, what should be his minimum constant acceleration? (b) How fast will Superman be traveling when he reaches Lois?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:52

Problem 30

During a walk on the Moon, an astronaut accidentally drops his camera over a 20.0-m cliff. It leaves his hands with zero speed, and after $2.0 \mathrm{~s}$ it has attained a velocity of $3.3 \mathrm{~m} / \mathrm{s}$ downward. How far has the camera fallen after $4.0 \mathrm{~s}$ ?

Sachin Rao
Sachin Rao
Numerade Educator
02:26

Problem 31

Glenda drops a coin from ear level down a wishing well. The coin falls a distance of $7.00 \mathrm{~m}$ before it strikes the
water. If the speed of sound is $343 \mathrm{~m} / \mathrm{s}$, how long after Glenda releases the coin will she hear a splash?

Sachin Rao
Sachin Rao
Numerade Educator
02:44

Problem 32

A stone is launched straight up by a slingshot. Its initial speed is $19.6 \mathrm{~m} / \mathrm{s}$ and the stone is $1.50 \mathrm{~m}$ above the ground when launched. (a) How high above the ground does the stone rise? (b) How much time elapses before the stone hits the ground?

Sachin Rao
Sachin Rao
Numerade Educator
12:07

Problem 33

A model rocket is fired vertically from rest. It has a net acceleration of $17.5 \mathrm{~m} / \mathrm{s}^{2}$. After $1.5 \mathrm{~s}$, its fuel is exhausted and its only acceleration is that due to gravity. (a) Ignoring air resistance, how high does the rocket travel?
(b) How long after liftoff does the rocket return to the ground?

Pronoy Sinha
Pronoy Sinha
Numerade Educator
14:01

Problem 34

The model rocket in Problem 33 has a mass of $87 \mathrm{~g}$ and you may assume the mass of the fuel is much less than 87 g. (a) What was the net force on the rocket during the first $1.5$ s after liftoff? (b) What force was exerted on the rocket by the burning fuel? (c) What was the net force on the rocket after its fuel was spent? (d) The rocket's vertical velocity was zero instantaneously when it was at the top of its trajectory. What were the net force and acceleration on the rocket at this instant?

Jose Carlos
Jose Carlos
Numerade Educator
05:30

Problem 35

You drop a stone into a deep well and hear it hit the bottom $3.20 \mathrm{~s}$ later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about $343 \mathrm{~m} / \mathrm{s}$ in air. How deep is the well?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
04:06

Problem 36

A baseball is thrown horizontally from a height of $9.60 \mathrm{~m}$ above the ground with a speed of $30.0 \mathrm{~m} / \mathrm{s}$. Where is the ball after $1.40 \mathrm{~s}$ have elapsed?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:01

Problem 37

A clump of soft clay is thrown horizontally from $8.50 \mathrm{~m}$ above the ground with a speed of $20.0 \mathrm{~m} / \mathrm{s}$. Where is the clay after $1.50 \mathrm{~s}$ ? Assume it sticks in place when it hits the ground.

Henrique Saito
Henrique Saito
Numerade Educator
06:50

Problem 38

A tennis ball is thrown horizontally from an elevation of $14.0 \mathrm{~m}$ above the ground with a speed of $20.0 \mathrm{~m} / \mathrm{s}$.
(a) Where is the ball after $1.60 \mathrm{~s}$ ? (b) If the ball is still in the air, how long before it hits the ground and where will it be with respect to the starting point once it lands?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:46

Problem 39

A ball is thrown from a point $1.0 \mathrm{~m}$ above the ground. The initial velocity is $19.6 \mathrm{~m} / \mathrm{s}$ at an angle of $30.0^{\circ}$ above the horizontal. (a) Find the maximum height of the ball above the ground. (b) Calculate the speed of the ball at the highest point in the trajectory.

Henrique Saito
Henrique Saito
Numerade Educator
06:52

Problem 40

An arrow is shot into the air at an angle of $60.0^{\circ}$ above the horizontal with a speed of $20.0 \mathrm{~m} / \mathrm{s}$. (a) What are the $x$ -and $y$ -components of the velocity of the arrow $3.0 \mathrm{~s}$ after it leaves the bowstring? (b) What are the $x$ - and $y$ components of the displacement of the arrow during the 3.0-s interval?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:27

Problem 41

You are working as a consultant on a video game designing a bomb site for a World War I airplane. In this game, the plane you are flying is traveling horizontally at $40.0 \mathrm{~m} / \mathrm{s}$ at an altitude of $125 \mathrm{~m}$ when it drops a bomb. (a) Determine how far horizontally from the target you should release the bomb. (b) What direction is the bomb moving just before it hits the target?

Henrique Saito
Henrique Saito
Numerade Educator
04:28

Problem 42

A ballplayer standing at home plate hits a baseball that is caught by another player at the same height above the ground from which it was hit. The ball is hit with an initial velocity of $22.0 \mathrm{~m} / \mathrm{s}$ at an angle of $60.0^{\circ}$ above the horizontal. ( Wh tutorial: projectile) (a) How high will the ball rise? (b) How much time will elapse from the time the ball leaves the bat until it reaches the fielder?
(c) At what distance from home plate will the fielder be when he catches the ball?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:52

Problem 43

You are planning a stunt to be used in an ice skating show. For this stunt a skater will skate down a frictionless ice
ramp that is inclined at an angle of $15.0^{\circ}$ above the horizontal. At the bottom of the ramp, there is a short horizontal section that ends in an abrupt drop off. The skater is supposed to start from rest somewhere on the ramp, then skate off the horizontal section and fly through the air a horizontal distance of $7.00 \mathrm{~m}$ while falling vertically for $3.00 \mathrm{~m}$, before landing smoothly on the ice. How far up the ramp should the skater start this stunt?

Henrique Saito
Henrique Saito
Numerade Educator
10:38

Problem 44

A suspension bridge is $60.0 \mathrm{~m}$ above the level base of a gorge. A stone is thrown or dropped from the bridge. Ignore air resistance. At the location of the bridge $g$ has been measured to be $9.83 \mathrm{~m} / \mathrm{s}^{2}$. (a) If you drop the stone, how long does it take for it to fall to the base of the gorge? (b) If you throw the stone straight down with a speed of $20.0 \mathrm{~m} / \mathrm{s}$, how long before it hits the ground?
(c) If you throw the stone with a velocity of $20.0 \mathrm{~m} / \mathrm{s}$ at $30.0^{\circ}$ above the horizontal, how far from the point directly below the bridge will it hit the level ground?

Vishal Gupta
Vishal Gupta
Numerade Educator
08:26

Problem 45

From the edge of the rooftop of a building, a boy throws a stone at an angle $25.0^{\circ}$ above the horizontal. The stone hits the ground $4.20 \mathrm{~s}$ later, $105 \mathrm{~m}$ away from the base of the building. (Ignore air resistance.) (a) For the stone's path through the air, sketch graphs of $x, y, v_{x}$, and $v_{y}$ as functions of time. These need to be only quali. tatively correct -you need not put numbers on the axes.
(b) Find the initial velocity of the stone. (c) Find the initial height $h$ from which the stone was thrown. (d) Find the maximum height $H$ reached by the stone.

Henrique Saito
Henrique Saito
Numerade Educator
04:10

Problem 46

Jason is practicing his tennis stroke by hitting balls against a wall. The ball leaves his racquet at a height of $60 \mathrm{~cm}$ above the ground at an angle of $80^{\circ}$ with respect to the vertical. (a) The speed of the ball as it leaves the racquet is $20 \mathrm{~m} / \mathrm{s}$ and it must travel a distance of $10 \mathrm{~m}$ before it reaches the wall. How far above the ground does the ball strike the wall? (b) Is the ball on its way up or down when it hits the wall?

Henrique Saito
Henrique Saito
Numerade Educator
05:53

Problem 47

You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located $5.0 \mathrm{~m}$ lower than the muzzle of the cannon from which the Great Flyinski is launched. The cannon will shoot the Great Flyinski at an angle of $35.0^{\circ}$ above the horizontal and at a speed of $18.0 \mathrm{~m} / \mathrm{s}$. The ringmaster
has asked that you decide how far from the cannon to place the net so that the Great Flyinski will land in the net and not be splattered on the floor, which would greatly disturb the audience. What do you tell the ringmaster? ( W interactive: projectile motion)

Vishal Gupta
Vishal Gupta
Numerade Educator
03:45

Problem 48

A circus performer is shot out of a cannon and flies over a net that is placed horizontally $6.0 \mathrm{~m}$ from the cannon. When the cannon is aimed at an angle of $40^{\circ}$ above the horizontal, the performer is moving in the horizontal direction and just barely clears the net as he passes over it. What is the muzzle speed of the cannon and how high is the net?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:44

Problem 49

A cannonball is catapulted toward a castle. The cannonball's velocity when it leaves the catapult is $40 \mathrm{~m} / \mathrm{s}$ at an angle of $37^{\circ}$ with respect to the horizontal and the cannonball is $7.0 \mathrm{~m}$ above the ground at this time. (a) What is the maximum height above the ground reached by the cannonball? (b) Assuming the cannonball makes it over the castle walls and lands back down on the ground, at what horizontal distance from its release point will it land?
(c) What are the $x$ - and $y$ -components of the cannonball's velocity just before it lands? The $y$ -axis points up.

Dominador Tan
Dominador Tan
Numerade Educator
07:27

Problem 50

After being assaulted by flying cannonballs, the knights on the castle walls ( $12 \mathrm{~m}$ above the ground) respond by propelling flaming pitch balls at their assailants. One ball lands on the ground at a distance of $50 \mathrm{~m}$ from the castle walls. If it was launched at an angle of $53^{\circ}$ above the horizontal, what was its initial speed?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:13

Problem 51

The citizens of Paris were terrified during World War I when they were suddenly bombarded with shells fired from a long-range gun known as Big Bertha. The barrel of the gun was $36.6 \mathrm{~m}$ long and it had a muzzle speed of $1.46 \mathrm{~km} / \mathrm{s}$. When the gun's angle of elevation was set to $55^{\circ}$, what would be the range? For the purposes of solving this problem, ignore air resistance. (The actual range at this elevation was $121 \mathrm{~km}$; air resistance cannot be ignored for the high muzzle speed of the shells.)

Jonah Wagner
Jonah Wagner
Numerade Educator
04:15

Problem 52

The range $R$ of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its original altitude. In other words, the range is the distance between the launch point and the impact point on flat ground. A projectile is launched at $t=0$ with initial speed $v_{\mathrm{i}}$ at an angle $\theta$ above the horizontal.
(a) Find the time $t$ at which the projectile returns to its original altitude. (b) Show that the range is
$$
R=\frac{v_{\mathrm{i}}^{2} \sin 2 \theta}{g}
$$
[Hint: Use the trigonometric identity $\sin 2 \theta=$ $2 \sin \theta \cos \theta .]$

Henrique Saito
Henrique Saito
Numerade Educator
01:52

Problem 53

Use the expression in Problem 52 to find (a) the maximum range of a projectile with launch speed $v_{1}$ and (b) the launch angle $\theta$ at which the maximum range occurs.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:14

Problem 54

A projectile is launched at $t=0$ with initial speed $v_{i}$ at an angle $\theta$ above the horizontal. (a) What are $v_{x}$ and $v_{y}$ at
the projectile's highest point? (b) Find the time $t$ at which the projectile reaches its maximum height.
(c) Show that the maximum height $H$ of the projectile is
$$
H=\frac{\left(v_{\mathrm{i}} \sin \theta\right)^{2}}{2 g}
$$

Henrique Saito
Henrique Saito
Numerade Educator
06:16

Problem 55

Two angles are complementary when their sum is $90.0^{\circ}$. Find the ranges for two projectiles launched with identical initial speeds of $36.2 \mathrm{~m} / \mathrm{s}$ at angles of elevation above the horizontal that are complementary pairs. (a) For one trial, the angles of elevation are $36.0^{\circ}$ and $54.0^{\circ} .$ (b) For the second trial, the angles of elevation are $23.0^{\circ}$ and $67.0^{\circ} .$ (c) Finally, the angles of elevation are both set to $45.0^{\circ} .$ (d) What do you notice about the range values for each complementary pair of angles? At which of these angles was the range greatest?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:07

Problem 56

Oliver has a mass of $76.2 \mathrm{~kg}$. He is riding in an elevator that has a downward acceleration of $1.37 \mathrm{~m} / \mathrm{s}^{2}$. With what magnitude force does the elevator floor push upward on Oliver?

Averell Hause
Averell Hause
Carnegie Mellon University
01:11

Problem 57

Yolanda, whose mass is $64.2 \mathrm{~kg}$, is riding in an elevator th?t has an upward acceleration of $2.13 \mathrm{~m} / \mathrm{s}^{2}$. What force does she exert on the floor of the elevator?

Averell Hause
Averell Hause
Carnegie Mellon University
02:19

Problem 58

When on the ground, Ian's weight is measured to be $640 \mathrm{~N}$. When Ian is on an elevator, his apparent weight is $700 \mathrm{~N}$. What is the net force on the system (Ian and the elevator) if their combined mass is $1050 \mathrm{~kg}$ ?

Averell Hause
Averell Hause
Carnegie Mellon University
03:06

Problem 59

While on an elevator, Jaden's apparent weight is $550 \mathrm{~N}$. When he is on the ground, the scale reading is $600 \mathrm{~N}$. What is Jaden's acceleration?

Averell Hause
Averell Hause
Carnegie Mellon University
03:45

Problem 60

You are standing on a bathroom scale inside an elevator. Your weight is $140 \mathrm{lb}$, but the reading of the scale is $120 \mathrm{lb}$. (a) What is the magnitude and direction of the acceleration of the elevator? (b) Can you tell whether the elevator is speeding up or slowing down?

Averell Hause
Averell Hause
Carnegie Mellon University
02:12

Problem 61

Refer to Example 4.12. What is the apparent weight of the same passenger (weighing $598 \mathrm{~N}$ ) in the following situations? In each case, the magnitude of the elevator's acceleration is $0.50 \mathrm{~m} / \mathrm{s}^{2}$. (a) After having stopped at the fifteenth floor, the passenger pushes the eighth floor button; the elevator is beginning to move downward.
(b) The elevator is moving downward and is slowing down as it nears the eighth floor.

Averell Hause
Averell Hause
Carnegie Mellon University
02:25

Problem 62

Luke stands on a scale in an elevator that has a constant acceleration upward. The scale reads $0.960 \mathrm{kN}$. When Luke picks up a box of mass $20.0 \mathrm{~kg}$, the scale reads $1.200 \mathrm{kN}$. (The acceleration remains the same.)
(a) Find the acceleration of the elevator.
(b) Find Luke's weight.

Averell Hause
Averell Hause
Carnegie Mellon University
01:06

Problem 63

Felipe is going for a physical before joining the swim team. He is concerned about his weight, so he carries his scale into the elevator to check his weight while
heading to the doctor's office on the twenty-first floor of the building. If his scale reads $750 \mathrm{~N}$ while the elevator has an upward acceleration of $2.0 \mathrm{~m} / \mathrm{s}^{2}$, what does the nurse measure his weight to be?

Averell Hause
Averell Hause
Carnegie Mellon University
02:27

Problem 64

A drag racer crosses the finish line of a $400.0-\mathrm{m}$ track with a final speed of $104 \mathrm{~m} / \mathrm{s}$. (a) Assuming constant acceleration during the race, find the racer's time and the minimum coefficient of static friction between the
tires and the road. (b) If, because of bad tires or wet pavement, the acceleration were $30.0 \%$ smaller, how long would it take to finish the race?

Manish Kumar
Manish Kumar
Numerade Educator
03:38

Problem 65

An African swallow carrying a very small coconut is flying horizontally with a speed of $18 \mathrm{~m} / \mathrm{s}$. (a) If it drops the coconut from a height of $100 \mathrm{~m}$ above the Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance from the release point will the coconut strike the ground?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:59

Problem 66

A ball is thrown horizontally off the edge of a cliff with an initial speed of $20.0 \mathrm{~m} / \mathrm{s}$. (a) How long does it take for the ball to fall to the ground $20.0 \mathrm{~m}$ below? (b) How long would it take for the ball to reach the ground if it were dropped from rest off the cliff edge? (c) How long would it take the ball to fall to the ground if it were thrown at an initial velocity of $20.0 \mathrm{~m} / \mathrm{s}$ but $18^{\circ}$ below the horizontal?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:04

Problem 67

A marble is rolled so that it is projected horizontally off the top landing of a staircase. The initial speed of the marble is $3.0 \mathrm{~m} / \mathrm{s}$. Each step is $0.18 \mathrm{~m}$ high and $0.30 \mathrm{~m}$ wide. Which step does the marble strike first?

Henrique Saito
Henrique Saito
Numerade Educator
View

Problem 68

You are serving as a consultant for the newest James Bond film. In one scene, Bond must fire a projectile from a cannon and hit the enemy headquarters located on the top of a cliff $75.0 \mathrm{~m}$ above and $350 \mathrm{~m}$ from the cannon. The cannon will shoot the projectile at an angle of $40.0^{\circ}$ above the horizontal. The director wants to know what the speed of the projectile must be when it is fired from the cannon so that it will hit the enemy headquarters. What do you tell him? [Hint: Don't assume the projectile will hit the headquarters at the highest point of its flight.]

Henrique Saito
Henrique Saito
Numerade Educator
05:05

Problem 69

An airplane is traveling from New York to Paris, a distance of $5.80 \times 10^{3} \mathrm{~km}$. Ignore the curvature of the Earth.
(a) If the cruising speed of the airplane is $350.0 \mathrm{~km} / \mathrm{h}$, how much time will it take for the airplane to make the round-trip on a calm day? (b) If a steady wind blows from New York to Paris at $60.0 \mathrm{~km} / \mathrm{h}$, how much time will the round-trip take? (c) How much time will it take if there is a crosswind of $60.0 \mathrm{~km} / \mathrm{h}$ ?

Henrique Saito
Henrique Saito
Numerade Educator
06:02

Problem 70

In free fall, we assume the acceleration to be constant. Not only is air resistance ignored, but the gravitational field strength is assumed to be constant. From what
height can an object fall to the Earth's surface such that the gravitational field strength changes less than $1.000 \%$ during the fall?

Averell Hause
Averell Hause
Carnegie Mellon University
04:35

Problem 71

The graph for this problem shows the vertical velocity component $v_{v}$ of a bouncing ball as a function of time. The $y$ -axis points up. Answer these questions based on the data in the graph. (a) At what time does the ball reach its maximum height? (b) For how long is the ball in contact with the floor? (c) What is the maximum height of the ball? (d) What is the acceleration of the ball while in the air? (e) What is the average acceleration of the ball while in contact with the floor?

Wesley Hines
Wesley Hines
Numerade Educator
05:24

Problem 72

A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of $20.0 \mathrm{~m} / \mathrm{s}^{2}$. However, after $50.0 \mathrm{~s}$ of flight the engine fails. (a) What is the rocket's altitude when the engine fails? (b) When does it reach its maximum height? (c) What is the maximum height reached? [Hint: A graphical solution may be easiest.] (d) What is the velocity of the rocket just before it hits the ground?

Sachin Rao
Sachin Rao
Numerade Educator
02:10

Problem 73

A particle has a constant acceleration of $5.0 \mathrm{~m} / \mathrm{s}^{2}$ to the east. At time $t=0$, it is $2.0 \mathrm{~m}$ east of the origin and its velocity is $20 \mathrm{~m} / \mathrm{s}$ north. What are the components of its position vector at $t=2.0 \mathrm{~s}$ ?

Henrique Saito
Henrique Saito
Numerade Educator
05:32

Problem 74

A baseball batter hits a long fly ball that rises to a height of $44 \mathrm{~m}$. An outfielder on the opposing team can run at $7.6 \mathrm{~m} / \mathrm{s}$. What is the farthest the fielder can be from where the ball will land so that it is possible for him to catch the ball?

Vishal Gupta
Vishal Gupta
Numerade Educator
10:35

Problem 75

A $15-\mathrm{kg}$ crate starts at rest at the top of a $60.0^{\circ}$ incline. The coefficients of friction are $\mu_{\mathrm{s}}=0.40$ and $\mu_{\mathrm{k}}=0.30$. The crate is connected to a hanging $8.0-\mathrm{kg}$ box by an ideal rope and pulley. (a) As the crate slides down the incline, what is the tension in the rope? (b) How long does it take the crate to slide $2.00 \mathrm{~m}$ down the incline?
(c) To push the crate back up the incline at constant speed, with what force $P$ should Pauline push on the crate (parallel to the incline)? (d) What is the smallest mass that you could substitute for the $8.0-\mathrm{kg}$ box to keep the crate from sliding down the incline?

Jose Carlos
Jose Carlos
Numerade Educator
03:30

Problem 76

A beanbag is thrown horizontally from a dorm room window a height $h$ above the ground. It hits the ground
a horizontal distance $h$ (the same distance $h$ ) from the dorm directly below the window from which it was thrown. Ignoring air resistance, find the direction of the beanbag's velocity just before impact.

Henrique Saito
Henrique Saito
Numerade Educator
01:52

Problem 77

An unmarked police car starts from rest just as a speeding car passes at a speed of $v$. If the police car speeds up with a constant acceleration of $a$, what is the speed of the police car when it catches up to the speeder, who does not realize she is being pursued and does not vary her speed?

Sachin Rao
Sachin Rao
Numerade Educator
09:02

Problem 78

A seagull is flying horizontally $8.00 \mathrm{~m}$ above the ground at $6.00 \mathrm{~m} / \mathrm{s}$. The bird is carrying a clam in its beak and plans to crack the clamshell by dropping it on some rocks below. Ignoring air resistance, (a) what is the horizontal distance to the rocks at the moment that the seagull should let go of the clam? (b) With what speed relative to the rocks does the clam smash into the rocks?
(c) With what speed relative to the seagull does the clam smash into the rocks?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:52

Problem 79

The minimum stopping distance of a car moving at $30.0 \mathrm{mi} / \mathrm{h}$ is $12 \mathrm{~m}$. Under the same conditions (so that the maximum braking force is the same), what is the minimum stopping distance for $60.0 \mathrm{mi} / \mathrm{h}$ ? Work by proportions to avoid converting units.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
11:31

Problem 80

A car traveling at $29 \mathrm{~m} / \mathrm{s}(65 \mathrm{mi} / \mathrm{h})$ runs into a bridge abutment after the driver falls asleep at the wheel. (a) If the driver is wearing a seat belt and comes to rest within a $1.0-\mathrm{m}$ distance, what is his acceleration (assumed constant)? (b) A passenger who isn't wearing a seat belt is thrown into the windshield and comes to a stop in a distance of $10.0 \mathrm{~cm}$. What is the acceleration of the passenger?

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:44

Problem 81

Find the point of no return for an airport runway of $1.50 \mathrm{mi}$ in length if a jet plane can accelerate at $10.0 \mathrm{ft} / \mathrm{s}^{2}$ and decelerate at $7.00 \mathrm{ft} / \mathrm{s}^{2}$. The point of no return occurs when the pilot can no longer abort the takeoff without running out of runway. What length of time is available from the start of the motion in which to decide on a course of action?

Wesley Hines
Wesley Hines
Numerade Educator
03:57

Problem 82

A helicopter is flying horizontally at $8.0 \mathrm{~m} / \mathrm{s}$ and an altitude of $18 \mathrm{~m}$ when a package of emergency medical supplies is ejected horizontally backward with a speed of $12 \mathrm{~m} / \mathrm{s}$ relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?

Vishal Gupta
Vishal Gupta
Numerade Educator
09:12

Problem 83

A locust jumps at an angle of $55.0^{\circ}$ and lands $0.800 \mathrm{~m}$ from where it jumped. (a) What is the maximum height of the locust during its jump? Ignore air resistance.
(b) If it jumps with the same initial speed at an angle of $45.0^{\circ}$, would the maximum height be larger or smaller?
(c) What about the range? (d) Calculate the maximum height and range for this angle.

Henrique Saito
Henrique Saito
Numerade Educator
03:58

Problem 84

A toboggan is sliding down a snowy slope. The table shows the speed of the toboggan at various times during
its trip. (a) Make a graph of the speed as a function of time. (b) Judging by the graph, is it plausible that the toboggan's acceleration is constant? If so, what is the acceleration? (c) Ignoring friction, what is the angle of incline of the slope? (d) If friction is significant, is the angle of incline larger or smaller than that found in
(c)? Explain.

Shelby Mohamed
Shelby Mohamed
Numerade Educator
02:22

Problem 85

Show that for a projectile launched at an angle of $45^{\circ}$ the maximum height of the projectile is one quarter of the range (the distance traveled on flat ground).

Vishal Gupta
Vishal Gupta
Numerade Educator
12:13

Problem 86

An airtrack glider, $8.0 \mathrm{~cm}$ long, blocks light as it goes through a photocell gate. The glider is released from rest on a frictionless inclined track and the gate is positioned so that the glider has traveled $96 \mathrm{~cm}$ when it is in the middle of the gate. The timer gives a reading of $333 \mathrm{~ms}$ for the glider to pass through this gate. Friction is negligible. What is the acceleration (assumed constant) of the glider along the track?

David González Cornejo
David González Cornejo
Numerade Educator
02:47

Problem 87

You want to make a plot of the trajectory of a projectile. That is, you want to make a plot of the height $y$ of the projectile as a function of horizontal distance $x$. The projectile is launched from the origin with an initial speed $v_{i}$ at an angle $\theta$ above the horizontal. Show that the equation of the trajectory followed by the projectile is
$$
y=\left(\frac{v_{\mathrm{iy}}}{v_{\mathrm{i} x}}\right) x+\left(\frac{-g}{2 v_{\mathrm{i}}^{2}}\right) x^{2}
$$

Henrique Saito
Henrique Saito
Numerade Educator
05:57

Problem 88

Locusts can jump to heights of $0.30 \mathrm{~m}$. (a) Assuming the locust jumps straight up, and ignoring air resistance, what is the takeoff speed of the locust? (b) The locust actually jumps at an angle of about $55^{\circ}$ to the horizontal, and air resistance is not negligible. The result is that the takeoff speed is about $40 \%$ higher than the value you calculated in part (a). If the mass of the locust is $2.0 \mathrm{~g}$ and its body moves $4.0 \mathrm{~cm}$ in a straight line while accelerating from rest to the takeoff speed, calculate the acceleration of the locust (assumed constant). (c) Ignore the locust's weight and estimate the force exerted on the hind legs by the ground. Compare this force with the locust's weight. Was it reasonable to ignore the locust's weight?

Alex Garger
Alex Garger
Numerade Educator
15:14

Problem 89

In Fig. $4.3$, the block of mass $m_{1}$ slides to the right with coefficient of kinetic friction $\mu_{\mathrm{k}}$ on a horizontal surface. The block is connected to a hanging block of mass $m_{2}$ by a light cord that passes over a light, frictionless pulley. (a) Find the acceleration of each of the blocks and the tension in the cord. (b) Check your answers in the special cases $m_{1} \ll m_{2}, m_{1} \gg m_{2}$, and $m_{1}=m_{2} .$ (c) For what value of $m_{2}$ (if any) do the two blocks slide at constant velocity? What is the tension in the cord in that case?

Cheng Zhao
Cheng Zhao
Numerade Educator
10:42

Problem 90

When salmon head
upstream to spawn, they often must make their way up a waterfall. If the
water is not mov-
ing too fast, the
salmon can swim
right up through the falling water. If the water is falling with too great a speed, the salmon jump out of the water to get to a place in the waterfall where the water
is not falling so fast. When humans build dams that interrupt the usual route followed by the salmon, artificial fish ladders must also be built to allow the salmon to get back uphill to the spawning area. These fish ladders consist of a series of small waterfalls with still pools of water in between them (see the figure). Assume that the water is at rest in the pools at the top and bottom of one "rung" of the fish ladder, that water falls straight down from one pool to the next, and that salmon can swim at $5.0 \mathrm{~m} / \mathrm{s}$ with respect to the water.
(a) What is the maximum height of a waterfall up which the salmon can swim without having to jump?
(b) If a waterfall is $1.5 \mathrm{~m}$ high, how high must the salmon jump to get to water through which it can swim? Assume that they jump straight up. (c) What initial speed must a salmon have to jump the height found in part (b)? (d) For a $1.0$ -m-high waterfall, how fast will the salmon be swimming with respect to the ground when it starts swimming up the waterfall?

Jonah Wagner
Jonah Wagner
Numerade Educator
06:19

Problem 91

Your current case as an FBI investigator involves a possible assassination attempt. The crime scene is a tall building, about $150 \mathrm{~m}$ high. As a foreign official was walking into the building, a flowerpot fell from above him and nearly landed on his head. One witness says that someone accidentally knocked the flowerpot from
a twenty-fourth-story window, $94 \mathrm{~m}$ above the ground. Another witness was inside the building looking out of an eighteenth-story window when she saw the flowerpot fall. She claims that the flowerpot took exactly $0.044 \mathrm{~s}$ to fall from the top of the window to the bottom of the window, a distance of $1.5 \mathrm{~m}$. (She knows this because she was videotaping her pet dachshund doing tricks and the flowerpot falling past the window was filmed in the background.) The top of the eighteenthstory window is $75 \mathrm{~m}$ above the ground. Could the flowerpot have fallen with zero initial velocity from the twenty-fourth-story window?

Dading Chen
Dading Chen
Numerade Educator
02:32

Problem 92

Jesse James and his gang are planning to rob the train carrying the payroll from the Lost Gulch mine. A Wells Fargo guard on the train spots Jesse astride his horse at a perpendicular distance of $0.300 \mathrm{~km}$ from the train tracks. The train is moving at $25.0 \mathrm{~m} / \mathrm{s}$ on a straight track. The guard wants to frighten Jesse and the desperadoes away by shooting a hole in Jesse's ten-gallon hat, which happens to be at the same height as the guard's gun (see the figure). The muzzle velocity of the guard's gun is $0.350 \mathrm{~km} / \mathrm{s}$. Ignore air resistance. (a) Should he aim the gun directly at Jesse's hat, in front of the hat, or behind the hat? Explain. (b) Unsure of the correct angle to aim the gun, the guard decides to aim his gun at a right angle to the track and fire the bullet a little before the time when he will be directly opposite to Jesse. At what distance before the point where the guard is directly opposite Jesse James should the guard fire? (c) Does the guard need to worry about the force of gravity on the bullet? If so, how far above the hat should he aim?

Chai Santi
Chai Santi
Numerade Educator