Chapter A.1, Problem 84E

Solution

How long does it take for the rock to fall a distance of 200m?

6.345 seconds.

Given:

The time t (in seconds) that it takes for a rock to fall a distance d (in meter) is approximately $t=0.45\sqrt{d}$ .

Calculation:

Time taken for a rock to fall a distance d, $t=0.45\sqrt{d}$

Time taken for a rock to fall a distance d=200m

  $\begin{array}{c}t=0.45\sqrt{d}\\ t=0.45\sqrt{200}\\ t=0.45\sqrt{10\cdot 10\cdot 2}\\ t=0.45(10)\sqrt{2}\\ t=4.5\sqrt{2}\\ t=4.5(1.41)\\ t=6.345\end{array}$

Time taken for a rock to fall a distance d=200m is t = 6.345 seconds.