A ball is thrown straight up from the ground with speed v 0. At the same instant

Question

A ball is thrown straight up from the ground with speed v0. At the same instant, a second ball is dropped from rest from a height H, directly above the point where the first ball was thrown upward. There is no air resistance.

a) Find the time at which the two balls collide. Express your answer in terms of the variables H, v0, and appropriate constants.

b) Find the value of H in terms of v0 and g so that at the instant when the balls collide, the first ball is at the highest point of its motion. Express your answer in terms of the variables v0 and g.

Explanation / Answer

for ball 1

y = vo*t - 0.5*g**t^2

for ball 2

H-y = 0.5*g*t^2

1 + 2

H = Vo*t

t = H/VO

partb

ball 1

t = Vo/g

h = Vo^2/2g

ball 2

H - h = 0.5*g*t^2 = 0.5*g*Vo^2/g^2

H-h = Vo^2/2g

H = 2*Vo^2/g

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