# The maximum height reached by the ball.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.8, Problem 10E

(a)

To determine

## To find: The maximum height reached by the ball.

Expert Solution

The maximum height reached by the ball is 100ft .

### Explanation of Solution

Given information:

The height function of the ball is given by,

s=80t16t2

The maximum height of the ball is achieved when the velocity is zero.

The time required to reach the maximum height of the ball is achieved when the velocity is zero is calculated as,

s=80t16t2dsdt=8032t0=8032tt=2.5s

The maximum height reached by the ball is calculated as,

s=80t16t2=80(2.5)16(2.5)2=100ft

Therefore, the maximum height reached by the ball is 100ft .

(b)

To determine

### To find: The velocity of the ball.

Expert Solution

The velocity of the ball on its way up and down are 16m/s and 16m/s .

### Explanation of Solution

Given information:

The height function of the ball is given by,

s=80t16t2

The time required to reach the maximum height of the ball is achieved when the velocity is zero is calculated as,

s=80t16t2dsdt=8032t0=8032tt=2.5s

The time required by the ballto reach 96ft is calculated as,

s=80t16t296=80t16t2t=2and 3s

The velocity of the ball on its way up is calculated as,

s=80t16t2dsdt=8032tv=8032(2)v=16m/s

The velocity of the ball on its way down is calculated as,

s=80t16t2dsdt=8032tv=8032(3)v=16m/s

Therefore, the velocity of the ball on its way up and down are 16m/s and 16m/s .

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