# The time interval during which the ball is at least 32ft above the ground.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 115E
To determine

## The time interval during which the ball is at least 32ft above the ground.

Expert Solution

The ball is at least 32ft above the ground from 0s to3_.

### Explanation of Solution

Given:

A ball is thrown upward with an initial velocity of 16 ft/s from me top of a building 128 ft high. Its height h above the ground t seconds later is given by h=128+16t16t2.

Calculation:

To obtain the time interval during which the ball is at least 32ft above the ground, set h32 and solve this inequality.

That is, solve the inequality 128+16t16t232.

Simplify the above inequality as follows.

128+16t16t2320[Subtract 32 from both sides]96+16t16t20[Subtract 32 from both sides]16t216t960[Multiply by 1on both sides]t2t60[Divide by 16 on both sides](t+2)(t3)0[Factor the LHS]

Note that, here t represents time and hence, t0. Then, t+20.

Divide by t+2 on both sides of the inequality (t+2)(t3)0. Therefore,

t30t3

On combining the two inequalities t0and t3, it can be written that 0 t3.

Thus, ball is at least 32ft above the ground from 0s to3_.

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