Question

Assuming no air resistance, the time$\mathit{t}$ in seconds that it takes an object to fall$\mathit{h}$ feet can be determined$\mathit{t}\mathbf{=}\frac{\sqrt{\mathbf{h}}}{\mathbf{4}}$. If a skydiver jumps from an airplane and free falls$\mathbf{10}\mathit{s}$before opening the parachute, how many feet does she free fall?

Short answer

If a skydiver jumps from an airplane and free falls for 10 seconds before opening the parachute, she free falls for $\mathbf{1600}\mathit{f}\mathit{e}\mathit{e}\mathit{t}$.

Step-by-step solution

Step1. Given 

$t=\frac{\sqrt{h}}{4}$

$t=\frac{\sqrt{h}}{4}$

Step2. Write the relationship between the time t in seconds that it takes an object to fall from h feet.

The relationship between thetime$t$ in seconds that it takes an object to fall from$h$ feetis:

$t=\frac{\sqrt{h}}{4}$, where$t$ is the time in second and$h$ is the height from which the object is dropped.

Step3. Determine the height from which the skydiver jumps.

It is given that skydiver free fall for 10 seconds. Therefore, the value$t$is 10.

Substitute 10 for$t$in $t=\frac{\sqrt{h}}{4}$.

$\begin{array}{l}t=\frac{\sqrt{h}}{4}\\ 10=\frac{\sqrt{h}}{4}\\ 40=\sqrt{h}\\ {40}^2={\left(\sqrt{h}\right)}^2\\ 1600=h\end{array}$

Therefore, if a skydiver jumps from an airplane and free falls for 10 seconds before opening the parachute, she free falls for $1600feet$.