If you throw a ball weighing 0.5 kg  at a velocity 30 m/s and hit a bottle with a mass of 0.2 kg which reaches 33 m/s, what is the velocity of the ball after collision?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A ball that has a mass of 0.5 kg and is moving at 30 m/s strikes a bottle with a mass 0.2 kg. After the collision, the velocity of the bottle is 33 m/s. We have to determine the velocity of the ball after the collision.

Here, the law of conservation of momentum can be used. The total momentum of the system initially is equal to the total final momentum.

As the bottle is initially stationary, the momentum is 0. The momentum of the ball is 0.5*30 = 15 kg*m/s. The total initial momentum of the system is 15 kg*m/s.

After collision, the bottle moves with a velocity of 33 m/s. The momentum of the bottle is 0.2*33 = 6.6 kg*m/s. Let the velocity of the ball after collision be V, the momentum of the ball is 0.5*V.

The total momentum of the system does not change:

15 = 6.6 + 0.5*V

=> 0.5*V = 15 - 6.6 = 8.4

=> V = 8.4/0.5

=> V = 16.8 m/s

The velocity of the ball after the collision is 16.8 m/s.

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