A projectile is launched from a cannon that sits 4 feet off the ground at an initial velocity of 120 feet/sec. Find the impact velocity.
Assuming this is on earth and the rocket goes up vertically,
d = -16t^2 + 120t + 4
dd/dt = velocity = -32t + 120
when does it hit the ground?
0 = -16t^2 + 120t + 4
4t^2 - 30t - 1 = 0
t = (30 ± √916)/8
= 7.5332 or a negative which we'll reject
velocity = -32(7.5332) + 120 = -121.1
it will hit the ground at 121.1 ft/second
(the negative indicates downward motion)