Question

a ball is thrown vertically upward from the ground level with an initial velocity "Vo" - V sub zero

a. derive a formula for the time at w/c the ball hit the ground

b. use the formula to prove that the impact velocity by the ball is -Vo

Answer 1

h(t) = Vot - 1/2 a t^2
= t(Vo - a/2 t)

h=0 when t=0 or t=2Vo/a)

v(t) = Vo - at
at t=2Vo/a, v = Vo - a(2Vo/a) = -Vo

Makes sense, since the ball falls just as far as it rises.