The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is -16ft^2+16t+32 , where t is the time in seconds since the ball was kicked. How high above the ground is the balcony?

Question

A.
2 ft

B.
16 ft

C.
32 ft

D.
36 ft

Answer 1

To find the height of the balcony above the ground, we need to evaluate the height function at \( t = 0 \), since this represents the moment the ball is kicked (when it starts from the balcony).

The height function given is:

\[ h(t) = -16t^2 + 16t + 32 \]

Now, substituting \( t = 0 \):

\[ h(0) = -16(0)^2 + 16(0) + 32 = 0 + 0 + 32 = 32 \]

Therefore, the height of the balcony above the ground is \( \text{32 ft} \).

So the answer is:

C. 32 ft