my math problem

Question

A ball is thrown upward from the height of 12 feet with initial velocity of 60 feet per second. Determine the maximum height the ball has reached. Find the time when the ball has reached the maximum height.

Answer 1

h(t) = -16t^2 +60t + 12

h'(t) =-32t +60 = 0

t = 60/32 = 15/8 seconds to reach max height

h(15/8) = max height = -16(15/8)^2 +60(15/8) +12

= -225/4 + 450/4 +12

= 225/4 +12

= 56 1/4 +12

= 68 1/4 feet = maximum height