Question

A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of $2.5 \mathrm{m}$ onto a concrete surface, a ball must rebound to a height of $1.4 \mathrm{m} .$ During impact, the ball compresses by approximately $6 \mathrm{mm}$. How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.) A. $5 \mathrm{m} / \mathrm{s}$ B. $7 \mathrm{m} / \mathrm{s}$ C. $25 \mathrm{m} / \mathrm{s}$ D. $50 \mathrm{m} / \mathrm{s}$

Name: Problem 90, Chapter 10: College Physics: A Strategic Approach
Uploaded: 2021-03-12T07:19:30-08:00
Duration: 46 s
Channel: Khoobchandra Agrawal

   A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of $2.5 \mathrm{m}$ onto a concrete surface, a ball must rebound to a height of $1.4 \mathrm{m} .$ During impact, the ball compresses by approximately $6 \mathrm{mm}$.
How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.)
A. $5 \mathrm{m} / \mathrm{s}$
B. $7 \mathrm{m} / \mathrm{s}$
C. $25 \mathrm{m} / \mathrm{s}$
D. $50 \mathrm{m} / \mathrm{s}$

College Physics: A Strategic Approach

Randall D. Knight,… 4th Edition

Chapter 10, Problem 90

Instant Answer

Solved by Expert Khoobchandra Agrawal

03/12/2021

Step 1

We can use the following kinematic equation to do this: v^2 = u^2 + 2as where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, due to gravity), and s is the distance traveled. In this problem, we have: - v = 0 m/s (the Show more…

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A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of $2.5 \mathrm{m}$ onto a concrete surface, a ball must rebound to a height of $1.4 \mathrm{m} .$ During impact, the ball compresses by approximately $6 \mathrm{mm}$. How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.) A. $5 \mathrm{m} / \mathrm{s}$ B. $7 \mathrm{m} / \mathrm{s}$ C. $25 \mathrm{m} / \mathrm{s}$ D. $50 \mathrm{m} / \mathrm{s}$

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Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position within a gravitational field. When an object is elevated, it stores energy which is converted into kinetic energy as it falls, a key principle in evaluating motions involving heights.

Energy Conservation in Free Fall

In free fall, particularly when air resistance is negligible, mechanical energy is conserved. This means the potential energy lost by an object moving downwards is completely converted into kinetic energy, allowing us to relate height to impact speed.

Kinematic Equations for Uniform Acceleration

Kinematic equations describe the motion of objects under constant acceleration. For free-falling objects, these equations allow one to compute the final speed from the drop height by relating acceleration due to gravity with the distance fallen without needing to know the time of fall.

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