Question

A skydiver jumped out of an airplane at the height of 10,000 feet. Assuming the initial velocity is zero, find the height of the skydiver 7 seconds after they step out of the airplane. Write a model, h(t)
that represents the height of the skydiver from the ground t seconds after they jump out of the airplane.(1 point)
Responses

9,888 feet
9,888 feet

9,759.9 feet
9,759.9 feet

9,126 feet
9,126 feet

69,216 feet

Answer 1

When modeling the height of a skydiver after jumping from an airplane, we can use the following physics-based equation for free fall under the influence of gravity.

The height \( h(t) \) of the skydiver at time \( t \) seconds after jumping can be modeled by the equation:

\[
h(t) = h_0 - \frac{1}{2} g t^2
\]

where:
- \( h_0 \) is the initial height (10,000 feet),
- \( g \) is the acceleration due to gravity (approximately 32 feet/s² on Earth),
- \( t \) is the time in seconds.

Substituting the values into the equation:

1. The initial height \( h_0 = 10,000 \) feet.
2. The acceleration due to gravity \( g = 32 \) feet/s².
3. We'll calculate for \( t = 7 \) seconds.

Plugging in these values, we calculate:

\[
h(7) = 10,000 - \frac{1}{2} \times 32 \times 7^2
\]

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Now calculating \( \frac{1}{2} \times 32 \times 49 \):

\[
\frac{1}{2} \times 32 = 16
\]

Then:

\[
16 \times 49 = 784
\]

Now substituting that back into the height equation:

\[
h(7) = 10,000 - 784 = 9,216
\]

To summarize, the height of the skydiver 7 seconds after they jump out of the airplane is:

\[
\boxed{9,216 \text{ feet}}
\]

Based on the provided options, "9,126 feet" would be the closest, but our calculation yields a slightly higher value. Therefore, none of the responses directly match our calculation.