The time taken by ball to fall half the distance to ground level if it is dropped from 96 ft 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 1.5, Problem 110E

(a)

To determine

The time taken by ball to fall half the distance to ground level if it is dropped from 96 ft above the ground.

Expert Solution

The time taken by ball to fall half the distance to ground level is 1.73s_.

Explanation of Solution

Given:

The height of an object dropped from a height h0 above the ground after t seconds is given by h=16t2+h0 where h is measured in feet.

Calculation:

It is given that the ball is dropped from 96 ft above the ground.

The height of the ball will be 962=48ft when it reaches half the distance to ground level.

Substitute 48 for h and 96ft for h0 in the equation h=16t2+h0.

48=16t2+9616t2=48t2=4816t2=3

Simplify further as follows.

t=±3t=±1.73

Note that, time will always be positive.

Thus, the time taken by ball to fall half the distance to ground level is 1.73s_.

(b)

To determine

The time taken by the ball to fall to the ground level.

Expert Solution

The time taken by the ball to fall to ground level is 2.5s_.

Explanation of Solution

It is given that the ball is dropped from 96 ft above the ground.

The height of the ball will be zero when it reaches the ground.

Therefore, substitute 0 for h and 96ft for h0 in the equation h=16t2+h0.

0=16t2+9616t2=96t2=9616t2=6

Simplify further as follows.

t=±6t=±2.45

Note that, time will always be positive.

Thus, the time taken by the ball to fall to ground level is 2.45s_.

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