Question

14. Martha dives into a swimming pool from a diving board that is 15 feet above the water. Her initial upward velocity is 5 feet per second. The function h(t)=−16t2+5t+15%0D%0Aℎ%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A−%0D%0A16%0D%0A%0D%0A2%0D%0A+%0D%0A5%0D%0A%0D%0A+%0D%0A15%0D%0Amodels Marthas height from the waters surface, where t represents time in seconds since she dove.(2 points)%0D%0AComplete the statements.%0D%0A%0D%0AThe interpretation of h(1) is that at %0D%0A, Marthas height is %0D%0A from the waters surface.

Answer 1

To interpret \( h(1) \) using the function \( h(t) = -16t^2 + 5t + 15 \):

1. Substitute \( t = 1 \) into the function to find her height at that time.
\[
h(1) = -16(1)^2 + 5(1) + 15
\]
\[
h(1) = -16 + 5 + 15
\]
\[
h(1) = -16 + 20
\]
\[
h(1) = 4
\]

2. Therefore, the interpretation of \( h(1) \) is:
- At \( t = 1 \) second, Martha's height is \( 4 \) feet from the water's surface.

So the completed statement would be:

"The interpretation of \( h(1) \) is that at **1 second**, Martha's height is **4 feet** from the water's surface."