Question

With what initial velocity must you throw a ball from a second-story window (h=4.0 m) in order for it to reach the ground in half the time it would have taken if it had been dropped and not thrown? -6.6m/s

Answer 1

H = 1/2 g T1^2 if ball is dropped

H = V0 T2 + 1/2 g T2^2 if ball has initial velocity

1/2 g T1^2 = V0 T2 + 1/2 g T2^2

T1 = 2 T2 T2 = T1 / 2

1/2 g (4 T2^2 - T2^2) = V0 T2

3/2 g T2^2 = V0 T2

V0 = 3/2 g T2

T1 = (2 H / g) ^1/2 if ball is dropped

T1 = (2 * 4 / g)^1/2 = .903 sec

T2 = .452

V0 = 3/2 g * .452 = 6.6 m/s if ball is thrown