Question

A rock is projected directly upward from ground level with an initial velocity of 90 ft per sec. The function in height of the rock in terms of time t is f (t) = −???? + ???. Find time t at which the rock reaches its maximum height and the maximum height in feet. Round answers to two decimal places, if necessary.

Answer 1

f(t) = - 16t^2 + 90t

Maximum height occurs at

t = - b/2a

t = - 90 / 2(-16) = 2.8125

Plug t = 2.8125 in the function

f(t) = - 16(2.8125)^2 + 90(2.8125)

126.5625

Time to reach maximum height is 2.81 seconds Maximum height = 126.56 feet