A tennis ball of mass 57.0 g is held just above a basketball...

A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g . With their centers vertically aligned, both are released from rest at the same moment, to fall through a distance of 1.20 m , as shown in Figure P9.20. (a) Find the magnitude of the downward velocity with which the basketball reaches the ground. Assume an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down. Next, the two balls meet in an elastic collision. (b) To what height does the tennis ball rebound?

Key Concepts

Free Fall Kinematics

This concept explains how objects accelerate downward under the influence of gravity, starting from rest. It involves using kinematic equations to relate the distance fallen, gravitational acceleration, and the final velocity before impact.

Conservation of Mechanical Energy

This principle states that in the absence of non-conservative forces like friction, the total energy of a system remains constant. For falling objects, gravitational potential energy is converted into kinetic energy, allowing the determination of velocity from a known drop height.

Elastic Collision Principles

In an elastic collision, both momentum and kinetic energy are conserved. This concept is key for analyzing interactions where colliding bodies, such as different mass sports balls, exchange speeds and directions without energy loss, such as during a rebound off the ground or mid-air collision.

Transcript

00:01 In this question are we have a tennis ball place on top of a basketball.

00:09 Okay, so the mass of the tens war is 57 grams and the mass off the basketball is 500 590 grams, and they are released from the height off, uh, 1.2 meters.

00:32 He so, in part a, we want to find our speed off the basketball, uh, 90 off the donald velocity off the basketball when it reaches the ground.

00:44 So we're using conservation of energy, okay, for the basketball earth system.

01:05 So hey, i plus your eye goes to kf us.

01:11 Us.

01:12 Ok, so i'm going to set you goes zero here, so, uh, usually okay, i throw plus mgh he goes the half empty square.

01:27 Uh, us, uh, zero.

01:32 So the you'll be square right to judge is equal to two times 9.8 times 1.2 square roots.

01:47 And this is four points.

01:50 It's five meters per second.

01:55 Okay, so this is the answer for part a killed in in practice be so give what happens is that both objects reached a bottom.

02:19 Okay, so the basketball collects plastic lee with the ground so it's going up before it's five meters per second and then the tennis for moving down before point.

02:31 It's five.

02:32 You just for a second.

02:33 So this is the before situation, okay? and after that, uh, the basketball would be moving down with re b and then a bus.

02:50 The tennis ball will be moving up with the treaty and parts of b b wants to find, uh, what's height? that's the tennis ball rebound.

03:00 Okay, so, um, that this is ah, conservation off momentum problem.

03:16 I'm going to take a word to be positive.

03:22 So we have empty times minus 4.85 plus and be, uh, for quite.

03:31 It's five it goes to and tv key plus and be really be, yeah, and then, since it's elastic collision so we have a relative speed approach.

03:54 He goes to relatives, be off separation.

04:06 Okay.

04:06 Which means that, um so our beauty minus baby, i secret too, uh, meaty.

04:18 I plus minus three b i because to, uh, meaty we be f minus ctf.

04:27 Okay, so, um, gain ticking upward to be positive, which gives us minus for its five minus 4.85 it goes to b minus vt.

04:48 So we have in this question, we are interested in vt.

04:52 So i'm going to substitute maybe in the conservation of momentum equation.

04:59 So rearranging i gets we because to 9.7 class beauty okay, i have to re christians...

Please give Ace some feedback