Determine the time the rock will reach it maximum height. What is the maximum height?

Question

A rock is propelled upward from the top of a building 110 feet tall at an initial velocity of 56 feet

per second. The function that describes the height of the rocket in terms of time t is

s(t)= - 16t 2 + 56t + 110. Determine the time at which the rock reaches its maximum height.

What is the maximum height?

Answer 1

s(t) = -16t^2 + 56t + 110

take the derivative, set = 0, and solve for t

s'(t) = -32t + 56 =0

t = 56/32 = 28/16 = 14/8= 7/4 = 1.75 seconds to reach max height

plug that into the original equation to solve for the maximum height

s(t) = s(1.75)= s(7/4) = -16(7/4)^2 + 56(7/4) +110 = -49 + 98 + 110 = 159 feet