Question

The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is -16t^2 + 24t + 40 , where t is the time in seconds since the ball was kicked.

The balcony is ______ feet above the ground.

Answers

GPT-4o mini
To find the height of the balcony above the ground, we need to evaluate the height equation at \( t = 0 \) seconds. This is because at \( t = 0 \), the ball has just been kicked and is still at the height of the balcony.

The height equation given is:

\[
h(t) = -16t^2 + 24t + 40
\]

Substituting \( t = 0 \):

\[
h(0) = -16(0)^2 + 24(0) + 40
\]
\[
h(0) = 0 + 0 + 40
\]
\[
h(0) = 40
\]

Therefore, the balcony is **40 feet** above the ground.