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
models Marthas height from the waters surface, where t represents time in seconds since she dove.(2 points)
Complete the statements.
The interpretation of h(1) is that at
, Marthas height is
from the waters surface.
models Marthas height from the waters surface, where t represents time in seconds since she dove.(2 points)
Complete the statements.
The interpretation of h(1) is that at
, Marthas height is
from the waters surface.
Answers
GPT-4o mini
To interpret \( h(1) \), we first need to evaluate the function \( h(t) \) at \( t = 1 \).
Given the function:
\[
h(t) = -16t^2 + 5t + 15
\]
Substituting \( t = 1 \):
\[
h(1) = -16(1)^2 + 5(1) + 15
\]
\[
h(1) = -16 + 5 + 15
\]
\[
h(1) = -16 + 20
\]
\[
h(1) = 4
\]
Now, we can complete the statements:
The interpretation of \( h(1) \) is that at **1 second**, Martha's height is **4 feet** from the water's surface.
Given the function:
\[
h(t) = -16t^2 + 5t + 15
\]
Substituting \( t = 1 \):
\[
h(1) = -16(1)^2 + 5(1) + 15
\]
\[
h(1) = -16 + 5 + 15
\]
\[
h(1) = -16 + 20
\]
\[
h(1) = 4
\]
Now, we can complete the statements:
The interpretation of \( h(1) \) is that at **1 second**, Martha's height is **4 feet** from the water's surface.