Question

A rubber ball is shot straight up from the ground with speed v0. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest.

Part A. At what height above the ground do the balls collide? Your answer will be a symbolic expression in terms of v0, h, and g .

Part B.

What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?

Express your answer in terms of the variable v0 and appropriate constants.

Part C.

For what value of h does the collision occur at the instant when the first ball is at its highest point?

Express your answer in terms of the variable v0 and appropriate constants.

Answer 1

a) from teh kinematic equation , the height reached by first ball
H = v₀t - gt²/2

the height reached by second ball is

h - H = gt²/2

add above two eqations

h = v₀t, t = h/v₀

H = h - gt²/2 = h - g(h/v₀)²/2 = h[1 - gh/(2v₀²)]

b)

H = 0,

so h = 2v₀²/g

c)

the time taken to reach heighest point is

t = v₀/g

the maximum heght reached by the ball is

H = v₀²/g

substitue values in the equation

h = H + gt²/2

   = v₀²/g + g(v₀/g)²/2

    = 3v₀²/(2g)