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Physics / Physics with MasteringPhysics 4 / Chapter 2 / Problem 114GP

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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A ball, dropped from rest, covers three-quarters of the

Chapter 2, Problem 114GP

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QUESTION:

A ball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall. (a) From what height was the ball dropped? (b) What was the total time of fall?

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QUESTION:

A ball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall. (a) From what height was the ball dropped? (b) What was the total time of fall?

ANSWER:

Step 1 of 2

Part a

We are required to calculate the height from which the ball was dropped

Let us consider the following figure for understanding the case.

The ball covers $h/4$ distance in (t-1) s and the rest $3h/4$ distance in 1 s, considering the total time taken is $t$ . Let total distance to the ground is $h$ .

Therefore,

$h/4=\frac{1}{2}g(t-1{)}^{2}$ …..(1)

And, $h=\frac{1}{2}g{t}^{2}$ …..(2)

Divide equation (1) by (2),

$\frac{h/4}{h}=(\frac{t-1}{t}{)}^{2}$

$\frac{1}{2}=\frac{t-1}{t}$

$2t-2=t$

$t=2$ s

Therefore, from $h=\frac{1}{2}g{t}^{2}$

$h=\frac{1}{2}\times{}9.81\times{}{2}^{2}$ m

$h=19.62$ m

Therefore, the height of the fall is 19.6 m.

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