Question

A rock is launched into the air from the top of a 50 foot cliff at an initial velocity of 120 ft/sec What is the maximum height the rock will reach? (hint: Projectile motion formula is - 16t ^ 2 + vt + h

Answer 1

Explanation:

The rock reaches its maximum height when the velocity is zero

Given the equation modeled by the height given as:

h(t) = - 16t^2 + vt + h

If v = 120ft/s and h = 50

h(t) = - 16t^2 + 120t + 50

First calculate t

At max height dh/dt = 0

dh/dt = -32t + 120

-32t +120 = 0

-32t = -120

t = -120/-32

t = 3.75s

Substitute t = 3.75 into the equation for the heightt

h(t) = - 16t^2 + 120t + 50

h(3.75) = - 16(3.75)^2 + 120(3.75) + 50

h(3.75) = - 225+ 450+ 50

h(3.75) = - 225+ 500

h(3.75) = 275m

Hence the max height reached by the rock is 275m