Question

17) On board the international space station, a bouncy ball is thrown and collides head-on with another bouncy ball of three times the first one's mass. The collision is elastic. (a) What is the ratio of the final velocity of the lighter ball to its initial velocity? (b) What about the ratio of the heavier ball's final velocity to its the lighter ball's initial velocity? Use the first input box for your answer to (a) and the second for your answer to (b).

Answer 1

given the second heavier ball is 3 times the mass of lighter ball

Then from conservation of momentum one has

This can be written as

Since the ball 2 is at rest initially,

....(1)

Since the collision is elastic, from conservation of kinetic energy, one has

This gives

....(2)

Here i and f indices stand for the initial and final velocity of the masses

Equations 1 and 2 can be satisfied if

and

a) Therefore the ratio of the final velocity of the lighter ball to its initial velocity is

b)  the ratio of the heavier ball's final velocity to its the lighter ball's initial velocity is