Question

Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

Answer 1

Assuming that Jules kicks the ball completely vertically, then you can use one of the famous kinematics equations (I'll spare you the derivation here):

(v-final)^2 - (v-initial)^2 = 2*a*height

In your case, the ball's final velocity (at its maximum height) is zero! Your acceleration is -g = -32 feet per second per second, and your initial velocity is 25 feet per second. So you have:

height = - (25)^2 / (2*-32) = 625 / 64 = 9.77 feet

Hope that helps!