Question

Terminal Velocity The terminal velocity of a parachutist is directly proportional to the square root of his weight. A $160\text{-lb}$parachutist attains a terminal velocity of $9\text{\hspace{0.33em}mi}/\text{h}$. What is the terminal velocity of a parachutist weighing $240\text{lb}$?

Short answer

The terminal velocity for the parachutist is $11\text{\hspace{0.33em}mi}/\text{h}$.

Step-by-step solution

Step 1. Write the given information.

The terminal velocity of parachutist weighing $240\text{lb}$is $9\text{mi}/\text{h}$.

The terminal velocity is directly proportional to square root of the weight.

Step 2. Write the direct relationship.

Let the terminal velocity be v and the weight be w. So, the direct relationship is given by,

$v=k\sqrt{w}\mathrm{...}\left(1\right)$

Here, k is the constant of proportionality.

Substitute 160 for w and 9 for v in equation (1).

$\begin{array}{c}9=k\sqrt{160}\\ k=\frac{9}{\sqrt{160}}\\ =0.71\end{array}$

Step 3. Find the terminal velocity.

Substitute 0.71 for k and 240 for w in equation (1).

$\begin{array}{c}v=0.71\sqrt{240}\\ =10.99\\ =11\text{\hspace{0.33em}mi}/\text{h}\end{array}$

Thus, the terminal velocity for the parachutist is $11\text{mi}/\text{h}$.