Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(II) Here is something to try at a sporting event. Show that the maximum height $h$ attained by an objcct projected into the air, such as a baseball, football, or soccer ball, is approximately given by $h \approx 1.2 t^{2} \mathrm{m}$where $t$ is the total time of fight for the object in seconds Assume that the object returns to the same level as that from which it was launched, as in Fig. $42 .$ For example, if you maximum height attained was $h=1.2 \times(5.0)^{2}=30 \mathrm{m}$ . The beauty of this relation is that $h$ can be determinedwithout knowlcdge of the launch speed $v_{0}$ or launch angle $\theta_{0}$ .

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

1.2$t^{2}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

05:23

An object is launched vert…

03:58

A projectile fired from $y…

07:07

Landing on a Different Lev…

02:56

Altitude of a Launched Obj…

16:53

Time of flight, range, hei…

04:38

Involve vertical motion an…

06:50

01:47

Flight of a projectile An …

05:35

Trajectory properties Find…

01:06

The height of a projectile…

The formula for the height…

03:14

A projectile is launched a…

Okay, So our question says that it wants us to try something at a sporting event. And it says show that the maximum height H attained by an object projected into the air said to the baseball, football or soccer ball is approximately given by H is approximately 1.2 t squared meters which I have written here where t is the total time of flight for the object in seconds. Assume that the object returns to the same level as from that which was launched. Doesn't think you're 42. For example, if your maximum height attained was h equals 1.2 times 10 to the fifth meter square, 1.2 times five squared is equal to 30 meters. The beauty of this relation is that age can be determined without knowledge of the V not or the angle fate or not. Okay, so in order to do this, I'm going Tio, consider downward vertical component of the motion which will occur in half the total time, okay, and then also take. And that's because the time it takes for it to go up and then back down is the time it takes for it to get to the very, very top at the very peak and at the peak, the total time it is going to take for a default. I'm sorry. The time is going to take for it to fall back Down from the peak is half of the total time. Okay, which I can go ahead and write that here. So the time for it to fall down equals 1/2 the total time. Which one? Tisa gap. Multi for total. Okay. And then the equation that we're going to use is well, why? This is equation to Dutch 12 b. Why is equal to why not the initial y plus Vina in the wider action? What times time? Because of you, Meters per second, We wanted to be in meters are solution of meters. So it's times, time, times 1/2 the acceleration in the white direction, right times t squared acceleration times t squared will give us meters, which is about, uh, the units we're looking for. Okay. And this is the total time. All right, well, let's go ahead in. Ah, that's not the total time. That's just the time that we're considering in the generic equation. So now Let's go ahead and plug in what we have for our situation. Well, what? We're trying to figure out his H. Why not? Well, why not? What is what we're considering here To be the time it takes to fall from the peak. So are why not Here is going to be zero. Right? Okay, we're going to consider that to be zero v Not why we're going to consider the velocity initial velocity to be zeros that's going to be plus zero. And then this is going to be plus 1/2 a of lie. Well, we're dealing with gravity. Here's that's going to gravity and then t squared that we're going to be using the time it takes for it to fall downwards. So that's 1/2 the total time. Okay, so this is 1/2 the total time, okay? And that is squared. Yeah. So now if we go ahead and continue on here, 1/2 squared is 1/4. 1/4 time's 1/2 which is out front of the G is 1/8. So this is 1/8 G is 9.8 meters per second squared since its acceleration. Right. And then we have the total time here squared. Yes, this is approximately. If you take 9.8 divided by eight. That's approximately 1.2 Mrs T squared units is meters. So therefore, box, I'd anyway, in approving the solution.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:50

Using your own words, provide a detailed discussion of whycoming to rest…

05:08

A large box of mass M is moving on a horizontalsurface at speed v0. A sm…

03:26

Electricity is distributed from electrical substations toneighborhoods a…

02:27

7. A particle of charge 3x10-9 C is located at point (0,0) in acertain c…

03:01

1. The Trans-Alaskan pipeline is 1300 km long, reaching fromPrudhoe Bay …

01:20

In the Helmholtz coils experiment, the current flowing throughthe two co…

01:08

Sheena can row a boat at 3.30 mi/h in still water. She needs tocross a r…

05:22

If the intensity of an electromagnetic wave is 80 MW/m2, what isthe ampl…

05:21

A 2.00 kg frictionless block attached to an idealspring with force const…

02:47

A soap bubble of index of refraction 1.33 strongly reflects bothred (700…