BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 115E

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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