Q43. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given.

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

Step 2. Write the relationship between the time t in seconds that it takes an object to fall from h feet .

The relationship between the time t in seconds that it takes an object to fall from h feet is:

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

Step 3. 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 $t=\frac{\sqrt{h}}{4}$.

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

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