A ball that is dropped from a window hits the ground in 6 seconds. How high is the window? (Give your answer in feet; note that the acceleration due to gravity is 32 ft/s^2.)

Question

A ball that is dropped from a window hits the ground in 6 seconds. How high is the window? (Give your answer in feet; note that the acceleration due to gravity is 32 ft/s^2.)

Height =

Answer 1

dv/dt = a

dv = adt

Since a = 32 and is downward, we can say a = -32 when the frame of reference is at the window.

dv = -32dt

∫dv = ∫-32 dt

v = -32t + C

Since it was dropped v(0) = 0 therefore C = 0

v = -32t

dy/dt = v (where y is the position in the y-direction)

So dy/dt = -32t

dy = -32t dt

∫dy = ∫-32t dt

y = -16t² + C

Since we have made our frame of reference at the window, the y(0) = 0

Therefore C = 0

y(t) = -16t²

y(6) = -16(6)² = -576 ft