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A ball has a mass of 0.25 kg and is moving to the right at 1.0 m/s. It hits a ball of mass 0.15 kg that is initially at rest. After the collision, the 0.15 kg ball moves off to the right with a velocity of 0.75 m/s.

What is the final velocity of the 0.25 kg ball?

0.42 m/s to the right
0.42 m/s to the left
0.55 m/s to the right
0.55 m/s to the left

Explanation:

Using the conservation of law of momentum which states that the sum of momentum of bodies before collision is equal to the sum of the bodies after collision.

Momentum = Mass (M) * Velocity(V)

BEFORE COLLISION

Momentum of 0.25kg body moving at 1.0m/s = 0.25*1 = 0.25kgm/s

Momentum of 0.15kg body moving at 0.0m/s(body at rest) = 0kgm/s

AFTER COLLISION

Momentum of 0.25kg body moving at x m/s = 0.25* x= 0.25x kgm/s

x is the final velocity of the 0.25kg ball

Momentum of 0.15kg body moving at 0.75m/s(body at rest) =

0.15 * 0.75kgm/s = 0.1125 kgm/s

Using the law of conservation of momentum;

0.25+0 = 0.25x + 0.1125

0.25x = 0.25-0.1125

0.25x = 0.1375

x = 0.1375/0.25

x = 0.55m/s

Since the 0.15 kg ball moves off to the right after collision, the 0.25 kg ball will move at 0.55 m/s towards the right

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