IMPACT VELOCITY QUESTION

If a ball is thrown vertically upward from the roof of a 32 foot building with a velocity of 16 ft/sec, its height after t seconds is: s(t)=32+16t-16t^2

What is the velocity of the ball when it hits the ground (height = 0)?





thanks

See how long it takes to hit the ground:

s(t)=32+16t-16t^2 = 0 ==> t^2 - t - 2 = (t - 2)(t + 1) = 0 ==> t = 2 seconds

The velocity is v(t) = ds/dt = 16 - 32t

and at t=2, v(2) = 16 - 64 = -48 ft/sec (Answer; negative because it's going down)