Physics for Scientist and Engineers: A Strategic Approach

Randall Knight

Chapter 4

Kinematics in Two Dimensions - all with Video Answers

Educators

Chapter Questions

Problem 1

Problems 1 through 3 show a partial motion diagram. For each:
a. Complete the motion diagram by adding acceleration vectors.
b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don't forget to include enough information to make the problem complete and to state clearly what is to be found.
(FIGURE CANNOT COPY)

Lisa Tarman

Lisa Tarman

Numerade Educator

Problem 2

Problems 1 through 3 show a partial motion diagram. For each:
a. Complete the motion diagram by adding acceleration vectors.
b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don't forget to include enough information to make the problem complete and to state clearly what is to be found.
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 3

Problems 1 through 3 show a partial motion diagram. For each:
a. Complete the motion diagram by adding acceleration vectors.
b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don't forget to include enough information to make the problem complete and to state clearly what is to be found.
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 4

Consider a pendulum swinging back and forth on a string. Use a motion diagram analysis and a written explanation to answer the following questions.
a. At the lowest point in the motion, is the velocity zero or nonzero? Is the acceleration zero or nonzero? If these vectors aren't zero, which way do they point?
b. At the end of its arc, when the pendulum is at the highest point on the right or left side, is the velocity zero or nonzero? Is the acceleration zero or nonzero? If these vectors aren't zero, which way do they point?

Hubert Agamasu

Numerade Educator

Problem 5

A sailboat is traveling east at $5.0 \mathrm{m} / \mathrm{s} .$ A sudden gust of wind gives the boat an acceleration $$\vec{a}=\left(0.80 \mathrm{m} / \mathrm{s}^{2}, 40^{\circ} \text { north of east }\right)$$ What are the boat's speed and direction 6.0 s later when the gust subsides?

Lisa Tarman

Numerade Educator

Problem 6

A particle's trajectory is described by $x=\left(\frac{1}{2} t^{3}-2 t^{2}\right) \mathrm{m}$ and $y=\left(\frac{1}{2} t^{2}-2 t\right) \mathrm{m},$ where $t$ is in $\mathrm{s}$
a. What are the particle's position and speed at $t=0$ s and $t=4 \mathrm{s} ?$
b. What is the particle's direction of motion, measured as an angle from the $x$ -axis, at $t=0 \mathrm{s}$ and $t=4 \mathrm{s} ?$

Lisa Tarman

Numerade Educator

Problem 7

A flying saucer maneuvering with constant acceleration is observed with the positions and velocities shown in FIGURE EX4.7. What is the saucer's acceleration $\vec{a} ?$
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 8

A rocket-powered hockey puck moves on a horizontal frictionless table. FiGURE EX4.8 at the top of the next column shows graphs of $v_{x}$ and $v_{y},$ the $x$ - and $y$ -components of the puck's velocity. The puck starts at the origin.
a. In which direction is the puck moving at $t=2$ s? Give your answer as an angle from the $x$ -axis.
b. How far from the origin is the puck at $t=5$ s?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 9

A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.9. shows graphs of $v_{x}$ and $v_{y},$ the $x$ - and y-components of the puck's velocity. The puck starts at the origin.
a. What is the magnitude of the puck's acceleration?
b. How far from the origin is the puck at $t=0 \mathrm{s}, 5 \mathrm{s},$ and $10 \mathrm{s} ?$
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 10

A physics student on Planet Bxidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.10.
The ball's position is shown at 1 s intervals until $t=3$ s. At $t=1 \mathrm{s},$ the ball's velocity is $\vec{v}=(2.0 \hat{\imath}+2.0 \hat{\jmath}) \mathrm{m} / \mathrm{s}$
a. Determine the ball's velocity at $t=0 \mathrm{s}, 2 \mathrm{s}$, and $3 \mathrm{s}$
b. What is the value of $g$ on Planet Exidor?
c. What was the ball's launch angle?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 11

A ball thrown horizontally at 25 m/s travels a horizontal distance of $50 \mathrm{m}$ before hitting the ground. From what height was the ball thrown?

Vishal Gupta

Numerade Educator

Problem 12

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target $2.0 \mathrm{cm}$ below the aim point.
a. What was the bullet's flight time?
b. What was the bullet's speed as it left the barrel?

Lisa Tarman

Numerade Educator

Problem 13

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of $150 \mathrm{m} / \mathrm{s}$. How far short of the target should it drop the package?

Lisa Tarman

Numerade Educator

Problem 14

A sailor climbs to the top of the mast, 15 m above the deck, to look for land while his ship moves steadily forward through calm waters at $4.0 \mathrm{m} / \mathrm{s}$. Unfortunately, he drops his spyglass to the deck below.
a. Where does it land with respect to the base of the mast below him?
b. Where does it land with respect to a fisherman sitting at rest in his dinghy as the ship goes past? Assume that the fisherman is even with the mast at the instant the spyglass is dropped.

Lisa Tarman

Numerade Educator

Problem 15

Ted is sitting in his lawn chair when Stella flies directly overhead, going southeast at $100 \mathrm{m} / \mathrm{s}$. Five seconds later, a fire. cracker explodes 200 m east of Ted. What are the coordinates of the explosion in Stella's reference frame? Let Stella be at the origin, with her $x$ -axis pointing to the cast.

Lisa Tarman

Numerade Educator

Problem 16

A boat takes 3.0 hours to travel $30 \mathrm{km}$ down a river, then 5.0 hours to return. How fast is the river flowing?

Lisa Tarman

Numerade Educator

Problem 17

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 75 s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Lisa Tarman

Numerade Educator

Problem 18

Mary needs to row her boat across a $100-$ m-wide river that is flowing to the east at a speed of $3.0 \mathrm{m} / \mathrm{s} .$ Mary can row with a speed of $2.0 \mathrm{m} / \mathrm{s}$
a. If Mary rows straight north, where will she land?
b. Draw a picture showing her displacement due to rowing, her displacement due to the river's motion, and her net displacement.

Lisa Tarman

Numerade Educator

Problem 19

Susan, driving north at $60 \mathrm{mph}$, and Shawn, driving cast at 45 mph, are approaching an intersection. What is Shawn's speed relative to Susan's reference frame?

Lisa Tarman

Numerade Educator

Problem 20

FIGURE EXA.20 shows the angular-position-versus-time graph for a particle moving in a circle.
a. Write a description of the particle's motion.
b. Draw the angular-velocity-versus-time graph.
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 21

FIGURE EX4.21 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 22

FIGURE EX4.22 shows the angular-velocity-versus-time graph for a particle moving in a circle, starting from $\theta_{0}=0$ rad at $t=0$ s. Draw the angular-position-versus-time graph. Include an appropriate scale on both axes.
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 23

An old-fashioned single-play vinyl record rotates on a turn table at 45 rpm. What are (a) the angular velocity in $\mathrm{rad} / \mathrm{s}$ and (b) the period of the motion?

Lisa Tarman

Numerade Educator

Problem 24

The earth's radius is about 4000 miles. Kampala, the capital
of Uganda, and singapore are both nearly on the equator. The distance between them is 5000 miles.
a. Through what angle do you turn, relative to the earth, if you fly from Kampala to Singapore? Give your answer in both radians and degrees.
b. The flight from Kampala to Singapore takes 9 hours. What is the plane's angular velocity relative to the earth?

Lisa Tarman

Numerade Educator

Problem 25

A $300-$ m-tall tower is built on the equator. How much faster does a point at the top of the tower move than a point at the bottom? The earth's radius is $6400 \mathrm{km}$

Lisa Tarman

Numerade Educator

Problem 26

How fast must a plane fly along the earth's equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both $\mathrm{km} / \mathrm{hr}$ and mph. The earth's radius is $6400 \mathrm{km} .$

Lisa Tarman

Numerade Educator

Problem 27

To withstand "g-forces" of up to 10 g's, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a "human centrifuge." $10 \mathrm{g}$ 's is an acceleration of $98 \mathrm{m} / \mathrm{s}^{2} .$ If the length of the centrifuge arm is $12 \mathrm{m},$ at what speed is the rider moving when she experiences $10 \mathrm{g}^{\prime} \mathrm{s} ?$

Lisa Tarman

Numerade Educator

Problem 28

The radius of the earth's very nearly circular orbit around the sun is $1.5 \times 10^{11} \mathrm{m}$. Find the magnitude of the earth's (a) velocity, (b) angular velocity, and (c) centripetal acceleration as it travels around the sun. Assume a year of 365 days.

Lisa Tarman

Numerade Educator

Problem 29

Your roommate is working on his bicycle and has the bike upside down. He spins the 60 -cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?

Lisa Tarman

Numerade Educator

Problem 30

FIGURE EX4.30 shows the angular velocity graph of the crankshaft in a car. Draw a graph of the angular acceleration versus time. Include appropriate numerical scales on both axes.
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 31

FIGURE EX4.31 shows the angular acceleration graph of a turntable that starts from rest. Draw a graph of the angular velocity versus time. Include appropriate numerical scales on both axes.
(FIGURE CANNOT COPY)

Yaqub Khan

Numerade Educator

Problem 32

FIGURE EX4.32 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 33

a. FIGURE EX4.33a shows angular velocity versus time. Draw the corresponding graph of angular acceleration versus time.
b. FIGURE EX4.33b shows angular acceleration versus time. Draw the corresponding graph of angular velocity versus time. Assume $\omega_{0}=0$
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 34

A car speeds up as it turns from traveling due south to heading due east. When exactly halfway around the curve, the car's acceleration is $3.0 \mathrm{m} / \mathrm{s}^{2}, 20^{\circ}$ north of east. What are the radial and tangential components of the acceleration at that point?

Lisa Tarman

Numerade Educator

Problem 35

A 5.0 -m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in $20 \mathrm{s}$
a. Before slowing, what is the speed of a child on the rim?
b. How many revolutions does the merry-go-round make as it stops?

Lisa Tarman

Numerade Educator

Problem 36

A $3.0$ -cm-diameter crankshaft that is rotating at 2500 rpm comes to a halt in $1.5 \mathrm{s}$
a. What is the tangential acceleration of a point on the surface?
b. How many revolutions does the crankshaft make as it stops?

Lisa Tarman

Numerade Educator

Problem 37

An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration?

Lisa Tarman

Numerade Educator

Problem 38

A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of $0.50 \mathrm{rad} / \mathrm{s}^{2}$
a. What is the wheel's angular velocity, in $\mathrm{rpm}, 10$ s later?
b. How many revolutions does the wheel make during this time?

Lisa Tarman

Numerade Educator

Problem 39

A particle starts from rest at $\vec{r}_{0}=9.0 \hat{\jmath} \mathrm{m}$ and moves in the $x y-$ plane with the velocity shown in FIGURE P4.39. The particle passes through a wire hoop located at $\vec{r}_{1}=20 \hat{\imath} \mathrm{m},$ then continues onward.
a. At what time does the particle pass through the hoop?
b. What is the value of $v_{4 y},$ the $y$ -component of the particle's velocity at $t=4 \mathrm{s} ?$
c. Calculate and plot the particle's trajectory.
(FIGURE CANNOT COPY)

Yaqub Khan

Numerade Educator

Problem 40

A projectile's horizontal range on level ground is $R=$ $v_{0}^{2} \sin 2 \theta / g .$ At what launch angle or angles will the projectile land at half of its maximum possible range.

Lisa Tarman

Numerade Educator

Problem 41

a. A projectile is launched with speed $v_{0}$ and angle $\theta .$ Derive an expression for the projectile's maximum height $h$
b. A baseball is hit with a speed of $33.6 \mathrm{m} / \mathrm{s}$. Calculate its height and the distance traveled if it is hit at angles of $30.0^{\circ}$ $45.0^{\circ},$ and $60.0^{\circ}$

Lisa Tarman

Numerade Educator

Problem 42

A projectile is fired with an initial speed of $30 \mathrm{m} / \mathrm{s}$ at an angle of $60^{\circ}$ above the horizontal. The object hits the ground 7.5 s later.
a. How much higher or lower is the launch point relative to the point where the projectile hits the ground?
b. To what maximum height above the launch point does the projectile rise?
c. What are the magnitude and direction of the projectile's velocity at the instant it hits the ground?

Lisa Tarman

Numerade Educator

Problem 43

In the Olympic shotput event, an athlete throws the shot with an initial speed of $12.0 \mathrm{m} / \mathrm{s}$ at $a\quad40.0^{\circ}$ angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground.
a. How far does the shot travel?
b. Repeat the calculation of part (a) for angles $42.5^{\circ}, 45.0^{\circ}$ and $47.5^{\circ} .$ Put all your results, including $40.0^{\circ},$ in a table. At what angle of release does she throw the farthest?

Hubert Agamasu

Numerade Educator

Problem 44

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is $1 / 6$ of its value on earth. Suppose he hit the ball with a speed of $25 \mathrm{m} / \mathrm{s}$ at an angle $30^{\circ}$ above the horizontal.
a. How much farther did the ball travel on the moon than it would have on earth?
b. For how much more time was the ball in flight?

Lisa Tarman

Numerade Educator

Problem 45

A ball is thrown toward a cliff of height $h$ with a speed of
$30 \mathrm{m} / \mathrm{s}$ and an angle of $60^{\circ}$ above horizontal. It lands on the edge of the cliff 4.0 s later.
a. How high is the cliff?
b. What was the maximum height of the ball?
c. What is the ball's impact speed?

Lisa Tarman

Numerade Educator

Problem 46

A tennis player hits a ball $2.0 \mathrm{m}$ above the ground. The ball leaves his racquet with a speed of $20.0 \mathrm{m} / \mathrm{s}$ at an angle $5.0^{\circ}$ above the horizontal. The horizontal distance to the net is $7.0 \mathrm{m}$ and the net is $1.0 \mathrm{m}$ high. Does the ball clear the net? If so, by how much? If not, by how much does it miss?

Vishal Gupta

Numerade Educator

Problem 47

A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 4.0 $\mathrm{m}$ above the ground. The ball lands 25 m away.
a. What is his pitching speed?
b. As you think about it, you're not sure he threw the ball exactly horizontally. As you watch him throw, the pitches seem to vary from $5^{\circ}$ below horizontal to $5^{\circ}$ above horizontal. What is the range of speeds with which the ball might have left his hand?

Lisa Tarman

Numerade Educator

Problem 48

You are playing right field for the baseball team. Your team is up by one run in the bottom of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 65 m from home plate, you see a runner rounding third base and heading for home with the tying run. You throw the ball at an angle of $30^{\circ}$ above the horizontal with just the right speed so that the ball is caught by the catcher, standing on home plate, at the same height as you threw it. As you release the ball, the runner is 20.0 m from home plate and running full speed at $8.0 \mathrm{m} / \mathrm{s} .$ Will the ball arrive in time for your team's catcher to make the tag and win the game?

Lisa Tarman

Numerade Educator

Problem 49

You're $6.0 \mathrm{m}$ from one wall of a house. You want to toss a ball to your friend who is 6.0 m from the opposite wall. The throw and catch each occur $1.0 \mathrm{m}$ above the ground.
a. What minimum speed will allow the ball to clear the roof?
b. At what angle should you toss the ball?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 50

Sand moves without slipping at $6.0 \mathrm{m} / \mathrm{s}$ down a conveyer that is tilted at $15^{\circ} .$ The sand enters a pipe $3.0 \mathrm{m}$ below the end of the conveyer belt, as shown in $\mathrm{FIGURE}$ $\mathrm{P4.50}$. What is the horizontal distance $d$ between the conveyer belt and the pipe?
(FIGURE CANNOT COPY)

Vishal Gupta

Numerade Educator

Problem 51

King Arthur's knights fire a cannon from the top of the castle wall. The cannonball is fired at a speed of $50 \mathrm{m} / \mathrm{s}$ and an angle of $30^{\circ} .$ A cannonball that was accidentally dropped hits the moat below in $1.5 \mathrm{s}$
a. How far from the castle wall does the cannonball hit the ground?
b. What is the ball's maximum height above the ground?

Lisa Tarman

Numerade Educator

Problem 52

A stunt man drives a car at a speed of 20 $\mathrm{m} / \mathrm{s}$ off a 30 -m-high cliff. The road leading to the cliff is inclined upward at an angle of $20^{\circ}$
a. How far from the base of the cliff does the car land?
b. What is the car's impact speed?

Lisa Tarman

Numerade Educator

Problem 53

A cat is chasing a mouse. The mouse runs in a straight line at a speed of $1.5 \mathrm{m} / \mathrm{s} .$ If the cat leaps off the floor at a $30^{\circ}$ angle and a speed of $4.0 \mathrm{m} / \mathrm{s},$ at what distance behind the mouse should the cat leap in order to land on the poor mouse?

Lisa Tarman

Numerade Educator

Problem 54

An assembly line has a staple gun that rolls to the left at $1.0 \mathrm{m} / \mathrm{s}$ while parts to be stapled roll past it to the right at $3.0 \mathrm{m} / \mathrm{s} .$ The staple gun fires 10 staples per second. How far apart are the staples in the finished part?

Lisa Tarman

Numerade Educator

Problem 55

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction $30^{\circ}$ west of north while the ship B travels $20^{\circ}$ east of north at 25 mph.
a. What is the distance between the two ships two hours after they depart?
b. What is the speed of ship A as seen by ship B?

Lisa Tarman

Numerade Educator

Problem 56

A kayaker needs to paddle north across a 100 -m-wide harbor. The tide is going out, creating a tidal current that flows to the east at $2.0 \mathrm{m} / \mathrm{s} .$ The kayaker can paddle with a speed of $3.0 \mathrm{m} / \mathrm{s}$
a. In which direction should he paddle in order to travel straight across the harbor?
b. How long will it take him to cross?

Lisa Tarman

Numerade Educator

Problem 57

Mike throws a ball upward and toward the east at a $63^{\circ}$ angle with a speed of $22 \mathrm{m} / \mathrm{s}$. Nancy drives east past Mike at $30 \mathrm{m} / \mathrm{s}$ at the instant he releases the ball.
a. What is the ball's initial angle in Nancy's reference frame?
b. Find and graph the ball's trajectory as seen by Nancy.

Yaqub Khan

Numerade Educator

Problem 58

A sailboat is sailing due east at 8.0 mph. The wind appears to blow from the southwest at 12.0 mph.
a. What are the true wind speed and direction?
b. What are the true wind speed and direction if the wind appears to blow from the northeast at $12.0 \mathrm{mph} ?$

Lisa Tarman

Numerade Educator

Problem 59

While driving north at $25 \mathrm{m} / \mathrm{s}$ during a rainstorm you notice that the rain makes an angle of $38^{\circ}$ with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

Yaqub Khan

Numerade Educator

Problem 60

A plane has an airspeed of 200 mph. The pilot wishes to reach a destination 600 mi due east, but a wind is blowing at 50 mph in the direction $30^{\circ}$ north of east.
a. In what direction must the pilot head the plane in order to reach her destination?
b. How long will the trip take?

Lisa Tarman

Numerade Educator

Problem 61

A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.
a. What is the acceleration at the end of a test tube that is $10 \mathrm{cm}$ from the axis of rotation?
b. For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of $1.0 \mathrm{m}$ and stopped in a 1.0 -ms-long encounter with a hard floor?

Lisa Tarman

Numerade Educator

Problem 62

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30 s to speed up from rest to its top speed of 1 rotation every 1.3 s. The astronaut is strapped into a seat $6.0 \mathrm{m}$ from the axis.
a. What is the astronaut's tangential acceleration during the first $30 \mathrm{s} ?$
b. How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each $9.8 \mathrm{m} / \mathrm{s}^{2}$ of acceleration is $1 \mathrm{g}$

Lisa Tarman

Numerade Educator

Problem 63

A car starts from rest on a curve with a radius of $120 \mathrm{m}$ and accelerates at $1.0 \mathrm{m} / \mathrm{s}^{2} .$ Through what angle will the car have traveled when the magnitude of its total acceleration is $2.0 \mathrm{m} / \mathrm{s}^{2} ?$

Lisa Tarman

Numerade Educator

Problem 64

As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude $26^{\circ},$ and (b) a physics student in Fairbanks, Alaska, at latitude $65^{\circ} ?$ Ignore the revolution of the earth around the sun. The radius of the earth is $6400 \mathrm{km}$

Lisa Tarman

Numerade Educator

Problem 65

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is $6.37 \times 10^{6} \mathrm{m},$ and the altitude of a geosynchronous orbit is $3.58 \times 10^{7} \mathrm{m}(\approx 22,000 \text { miles }) .$ What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?

Lisa Tarman

Numerade Educator

Problem 66

A magnetic computer disk $8.0 \mathrm{cm}$ in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at $600 \mathrm{rad} / \mathrm{s}^{2}$ for $\frac{1}{2} \mathrm{s},$ then coasts at a steady angular velocity for another $\frac{1}{2}$ s. What is the speed of the dot at $t=1.0 \mathrm{s} ?$ Through how many revolutions has the disk turned?

Lisa Tarman

Numerade Educator

Problem 67

A high-speed drill rotating ccw at 2400 rpm comes to a halt in $2.5 \mathrm{s}$
a. What is the drill's angular acceleration?
b. How many revolutions does it make as it stops?

Lisa Tarman

Numerade Educator

Problem 68

An electric-generator turbine spins at $3600$ rpm. Friction is so small that it takes the turbine $10$ min to coast to a stop. How many revolutions does it make while stopping?

Lisa Tarman

Numerade Educator

Problem 69

A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE P4.69. What is the wheel's angular velocity, in rpm, at $t=3.0 \mathrm{s} ?$
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 70

If you step on your car's brakes hard, the wheels stop turning (i.e., the wheels "lock") after 1.0 revolution. At the same constant acceleration, how many revolutions do the wheels make before stopping if your initial speed is twice as high?

Lisa Tarman

Numerade Educator

Problem 71

A well-lubricated bicycle wheel spins a long time before stopping. Suppose a wheel initially rotating at 100 rpm takes 60 s to stop. If the angular acceleration is constant, how many revolutions does the wheel make while stopping?

Lisa Tarman

Numerade Educator

Problem 72

A rock stuck in the tread of a 60.0 -cm-diameter bicycle wheel has a tangential speed of $3.00 \mathrm{m} / \mathrm{s} .$ When the brakes are applied, the rock's tangential deceleration is $1.00 \mathrm{m} / \mathrm{s}^{2}$
a. What are the magnitudes of the rock's angular velocity and angular acceleration at $t=1.50 \mathrm{s} ?$
b. At what time is the magnitude of the rock's acceleration equal to $g$?

Yaqub Khan

Numerade Educator

Problem 73

A long string is wrapped around a $6.0$ -cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of $1.5 \mathrm{m} / \mathrm{s}^{2}$ until $1.0 \mathrm{m}$ of string has been unwound. If the string unwinds without slipping, what is the cylinder's angular speed, in $\mathrm{rpm}$, at this time?

Lisa Tarman

Numerade Educator

Problem 74

You are given the equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.
b. Finish the solution of the problem, including a pictorial representation.
$$\begin{aligned}
&100 \mathrm{m}=0 \mathrm{m}+(50 \cos \theta \mathrm{m} / \mathrm{s}) t_{1}\\
&0 \mathrm{m}=0 \mathrm{m}+(50 \sin \theta \mathrm{m} / \mathrm{s}) t_{1}-\frac{1}{2}\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right) t_{1}^{2}
\end{aligned}$$

Yaqub Khan

Numerade Educator

Problem 75

You are given the equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.
b. Finish the solution of the problem, including a pictorial representation.
$$\begin{array}{l}
v_{x}=-\left(6.0 \cos 45^{\circ}\right) \mathrm{m} / \mathrm{s}+3.0 \mathrm{m} / \mathrm{s} \\
v_{y}=\left(6.0 \sin 45^{\circ}\right) \mathrm{m} / \mathrm{s}+0 \mathrm{m} / \mathrm{s} \\
100 \mathrm{m}=v_{y} t_{1}, x_{1}=v_{x} t_{1}
\end{array}$$

Yaqub Khan

Numerade Educator

Problem 76

You are given the equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.
b. Finish the solution of the problem, including a pictorial representation.
$$\begin{array}{l}
2.5 \mathrm{rad}=0 \mathrm{rad}+\omega_{\mathrm{i}}(10 \mathrm{s})+\left(\left(1.5 \mathrm{m} / \mathrm{s}^{2}\right) / 2(50 \mathrm{m})\right)(10 \mathrm{s})^{2} \\
\omega_{\mathrm{f}}=\omega_{\mathrm{i}}+\left(\left(1.5 \mathrm{m} / \mathrm{s}^{2}\right) /(50 \mathrm{m})\right)(10 \mathrm{s})
\end{array}$$

Yaqub Khan

Numerade Educator

Problem 77

Write a realistic problem for which the $x$ -versus-$t$ and $y$ -versus-t graphs shown in FIGURE P4.77 represent the motion of an object. Be sure the answer your problem requests is consistent with the graphs. Then finish the solution of the problem.
(FIGURE CANNOT COPY)

Yaqub Khan

Numerade Educator

Problem 78

You are asked to consult for the city's research hospital, where a group of doctors is investigating the bombardment of cancer tumors with high-energy ions. The ions are fired directly toward the center of the tumor at speeds of $5.0 \times 10^{6} \mathrm{m} / \mathrm{s} .$ To cover the entire tumor area, the ions are deflected sideways by passing them between two charged metal plates that accelerate the ions perpendicular to the direction of their initial motion. The acceleration region is $5.0 \mathrm{cm}$ long, and the ends of the acceleration plates are $1.5 \mathrm{m}$ from the patient. What acceleration is required to deflect an ion $2.0 \mathrm{cm}$ to one side?
(FIGURE CANNOT COPY)

Yaqub Khan

Numerade Educator

Problem 79

In one contest at the county fair, a spring-loaded plunger launches a ball at a speed of $3.0 \mathrm{m} / \mathrm{s}$ from one corner of a smooth, flat board that is tilted up at a $20^{\circ}$ angle. To win, you must make the ball hit a small target at the adjacent corner, 2.50 m away. At what angle $\theta$ should you tilt the ball launcher?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 80

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground $60 \mathrm{m}$ away, making a $3^{\circ}$ angle with the ground. How fast was the arrow shot?

Lisa Tarman

Numerade Educator

Problem 81

An archer standing on a $15^{\circ}$ slope shoots an arrow $20^{\circ}$ above the horizontal, as shown in FIGURE CP4.81. How far down the slope does the arrow hit if it is shot with a speed of $50 \mathrm{m} / \mathrm{s}$ from $1.75 \mathrm{m}$ above the ground?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 82

A rubber ball is dropped onto a ramp that is tilted at $20^{\circ},$ as shown in FIGURE CP4.82. A bouncing ball obeys the "law of reflection," which says that the ball leaves the surface at the same angle it approached the surface. The ball's next bounce is $3.0 \mathrm{m}$ to the right of its first bounce. What is the ball's rebound speed on its first bounce?
(FIGURE CANNOT COPY)

Lisa Tarman

Numerade Educator

Problem 83

A skateboarder starts up a 1.0 -m-high, $30^{\circ}$ ramp at a speed of 7.0 $\mathrm{m} / \mathrm{s}$. The skateboard wheels roll without friction. How far from the end of the ramp does the skateboarder touch down?

Lisa Tarman

Numerade Educator

Problem 84

A motorcycle daredevil wants to set a record for jumping over burning school buses. He has hired you to help with the design. He intends to ride off a horizontal platform at $40 \mathrm{m} / \mathrm{s}$, cross the burning buses in a pit below him, then land on a ramp sloping down at $20^{\circ} .$ It's very important that he not bounce when he hits the landing ramp because that could cause him to lose control and crash. You immediately recognize that he won't bounce if his velocity is parallel to the ramp as he touches down. This can be accomplished if the ramp is tangent to his trajectory and if he lands right on the front edge of the ramp. There's no room for error! Your task is to determine where to place the landing ramp. That is, how far from the edge of the launching platform should the front edge of the landing ramp be horizontally and how far below it? There's a clause in your contract that requires you to test your design before the hero goes on national television to set the record.

Lisa Tarman

Numerade Educator

Problem 85

A cannon on a train car fires a projectile to the right with speed $v_{0},$ relative to the train, from a barrel elevated at angle $\theta .$ The cannon fires just as the train, which had been cruising to the right along a level track with speed $v_{\text {train }},$ begins to accelerate with acceleration $a$. Find an expression for the angle at which the projectile should be fired so that it lands as far as possible from the cannon. You can ignore the small height of the cannon above the track.

Yaqub Khan

Numerade Educator

Problem 86

A child in danger of drowning in a river is being carried downstream by a current that flows uniformly with a speed of $2.0 \mathrm{m} / \mathrm{s}$ The child is 200 m from the shore and 1500 m upstream of the boat dock from which the rescue team sets out. If their boat speed is $8.0 \mathrm{m} / \mathrm{s}$ with respect to the water, at what angle from the shore should the pilot leave the shore to go directly to the child?

Yaqub Khan

Numerade Educator

Problem 87

Uri is on a flight from Boston to Los Angeles. His plane is traveling $20^{\circ}$ south of west at 500 mph. Val is on a flight from Miami to Seattle. Her plane is traveling $30^{\circ}$ north of west at 500 mph. Somewhere over Kansas, Uri's plane passes $1000 \mathrm{ft}$ directly over Val's plane. Uri is sitting on the right side and can see Val's plane below him after they pass. Uri notices that the fuselage of Val's plane doesn't point in the direction that her plane is moving. What is the angle between the fuselage and the direction of motion?

Yaqub Khan

Numerade Educator

Problem 88

An amusement park game, shown in FIGURE CP4.88, launches a marble toward a small cup. The marble is placed directly on top of a spring-loaded wheel and held with a clamp. When released, the wheel spins around clockwise at constant angular acceleration, opening the clamp and releasing the marble after making $\frac{11}{12}$ revolution. What angular acceleration is needed for the ball to land in the cup?
(FIGURE CANNOT COPY)

Yaqub Khan

Numerade Educator