A rubber ball is shot straight up from the ground with speed v 0. Simultaneously

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.

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 .

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

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.

Explanation / Answer

(a)

For the 1st ball:

H = v0t - gt2/2

For the 2nd ball:

h - H = gt2/2

Add above two equations each other.

h = v0t, t = h/v0

Therefore,

H = h - gt2/2

    = h - g(h/v0)2/2

    = h[1 - gh/(2v02)]

(b)

Substitute H=0,

            h[1 - gh/(2v02)]=0

                      h = 2v02/g

(c)

At the highest point:

t = v0/g,

H = v02/g

Substitute those values in the equation.

h = H + gt2/2

   = v02/g + g(v0/g)2/2

   = 3v02/(2g)

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