Rebekah kicks a soccer ball off the ground and in the air with an initial velocity of 25 feet per second. Using the formula H(t) = −16t^2 + vt + s, what is the maximum height the soccer ball reaches?

Question

anonymous · Answer

9.8 feet

nathan917 · Answer

Here the equation is
-16t² + 25t + 0 (s = initial height = 0 as it is the ground)
We do not try to make it equal to 0, we try to know when it will reach a maximum height.
I cannot explain here ( it is a complete lesson) but you must derivate, and say the derivate equals 0.
You will find the time at which the ball will be at the maximum. Then you will plug this time in the equation and you will get the maximum height.

Derivative of -16t² + 25t =-32t + 25
-32t + 25 = 0
32t = 25
t = 25/32 sec. That is the time : less than one sec. It equals 0.7813 sec
To know the heigth, let's plug the time in the initial function
H = -16(0.7813)² + 25(0.7813) = -16( 0.6104) + 25(0.7813) =
= -9.767 + 19.533 = 9.766 = 9.8 feet