A skydiver drops her watch as she jumps
out of a plane flying at an altitude of 6,400
feet. If the equation for height as a
function of time is
initial height where is time in
secondst and is height in feet, how
many seconds will it take for the watch to
hit the ground?
[? ] seconds

Ask by Hardy Christensen. in the United States

Jan 23,2025

Question

A skydiver drops her watch as she jumps
out of a plane flying at an altitude of 6,400
feet. If the equation for height as a
function of time is
initial height where is time in
secondst and is height in feet, how
many seconds will it take for the watch to
hit the ground?
[? ] seconds

Ask by Hardy Christensen. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To determine how many seconds it will take for the watch to hit the ground, we'll use the given height equation:

$$
h(t) = -16t^2 + \text{initial height}
$$

Here:
- $$ h(t) $$ is the height in feet at time $$ t $$ seconds.
- The initial height is 6,400 feet.

Substitute the initial height into the equation:

$$
h(t) = -16t^2 + 6400
$$

We want to find the time $$ t $$ when the watch hits the ground, which means $$ h(t) = 0 $$:

$$
0 = -16t^2 + 6400
$$

Solving for $$ t $$:

$$
16t^2 = 6400 \
t^2 = \frac{6400}{16} \
t^2 = 400 \
t = \sqrt{400} \
t = 20 \text{ seconds}
$$

**Answer:**  
It will take 20 seconds for the watch to hit the ground.
It will take 20 seconds for the watch to hit the ground.