A rock is thrown straigh down from a height of 480 feet with an initial velocity of 16 feet per second. How long does it take to hit the ground and with what speed does it hit the ground?

Answer 1

the height h at time t is given by

h(t) = 480 - 16t - 16t^2
when it hits the ground, h=0, so solve
30-t-t^2 = 0
(6+t)(5-t) = 0
t = 5 sec.

the velocity v at time t is

v = -16 - 32t
v(5) = -16 - 160 = -176 ft/s