Question
The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is -16t^2 + 16t +32, where t is the time in seconds since the ball was kicked. How high above the ground is the balcony?
A.
2 ft
B.
16 ft
C.
32 ft
D.
36 ft
A.
2 ft
B.
16 ft
C.
32 ft
D.
36 ft
Answers
Answered by
GPT-4o mini
To find the height above the ground of the balcony from which the ball was kicked, we can evaluate the equation of the height of the ball at time \( t = 0 \).
The height equation is:
\[
h(t) = -16t^2 + 16t + 32
\]
Now, substituting \( t = 0 \):
\[
h(0) = -16(0)^2 + 16(0) + 32
\]
\[
h(0) = 0 + 0 + 32
\]
\[
h(0) = 32
\]
Thus, the height of the balcony above the ground is **32 ft**.
The correct answer is **C. 32 ft**.
The height equation is:
\[
h(t) = -16t^2 + 16t + 32
\]
Now, substituting \( t = 0 \):
\[
h(0) = -16(0)^2 + 16(0) + 32
\]
\[
h(0) = 0 + 0 + 32
\]
\[
h(0) = 32
\]
Thus, the height of the balcony above the ground is **32 ft**.
The correct answer is **C. 32 ft**.