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.

1 answer

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.