The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is -16t2+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

Answer 1

To find the height of the balcony from which the ball is kicked, we need to determine the height of the ball at time \( t = 0 \). This is because the height function gives the height of the ball starting from the moment it is kicked.

The height of the ball as a function of time is given by:

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

At \( t = 0 \):

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

So, the height of the balcony above the ground is 32 feet.

Therefore, the answer is C. 32 ft.