How do I find the velocity of the rock when it hit the ground?

Question

A rock is thrown into the air from atop a building, and its height at time t is given by the equation

h(t)= -16t^2+48t+60

What was the velocity of the rock when it hit the ground?

Any help would be greatly appreciated. Please show your work, Thanks!

Answer 1

First we need to find the time when the rock hits the ground, or h(t) = 0

-16t²+48t+60 = 0

Which is a quadratic equation

t = (-48 ±√(48² - 4(-16)(60))/(-32) = -0.45, 3.95

Use the positive value.

v(t) = dh/dt = -32t + 48

v(3.95) = -78.4 ft/s (The minus is because it is falling)

The units are in feet, because the acceleration of gravity ≈ -32 ft/s² and the formula given is:

h(t) = gt²/2 + v₀t + h₀