A 100g ball moving to the right at 4.2m/s catches up and collides with a 450g ba

Question

A 100g ball moving to the right at 4.2m/s catches up and collides with a 450g ball that is moving to the right at 1.0m/s.

A. If the collision is perfectly elastic, what is the speed of the 100g ball after the collision?

B. If the collision is perfectly elastic, what is the direction of motion of the 100

g ball after the collision?(left or right)

C. If the collision is perfectly elastic, what is the speed of the 450g

ball after the collision?

D. If the collision is perfectly elastic, what is the direction of motion of the 450

g ball after the collision? (left or right)

Explanation / Answer

Let the final speed of 100 gm ball is v1

and final speed of 450 g ball is v2

Using conservation of momentum ,

100v1 + 450v2 = 4.2 *100 + 450 * 1       --------(1)

Now , for elastic collision , e =1

4.2 -1 = v2 - v1      --------(2)

solving for v1 and v2

v1 = -1.04 m/s

v2 = 2.16 m/s

the speed of 100 g ball is 1.04 m/s to the left

and the speed if 450 gm ball is 2.16 m/s to the right

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