# Two balls with mass 3 kg and 13 kg moving in opposite directions at 4 m/s collide. The impact changes the angle at which the 13 kg ball is moving by 5 degrees to the original direction. What is the...

Two balls with mass 3 kg and 13 kg moving in opposite directions at 4 m/s collide. The impact changes the angle at which the 13 kg ball is moving by 5 degrees to the original direction. What is the angle by which the velocity of the other is changed. (Assume a perfectly elastic collision)

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### 1 Answer

Two balls moving at 4 m/s in opposite directions collide. The mass of one of the balls is 3 kg and the other has a mass of 13 kg. As a result of the collision, the ball with mass 13 kg moves in a direction that is at an angle of 5 degrees to the original path.

To determine the direction of the other ball use the law of conservation of momentum. Let the angle between the new direction of the ball and the original direction be X.

The momentum of the ball with mass 13 kg, can be divided into two components, one with the same direction as the original velocity and the other making an angle of 90 degrees with the original direction. The former is equal to 13*4*cos 5 and the latter is 13*4*sin 5. Similarly, the component of the new momentum of the ball with mass 3 kg in the direction perpendicular to its original direction is 3*4*sin X.

3*4*sin X = 13*4*sin 5

=> sin X = (13*sin 5)/3

=> X `~~` 22.18

The ball with mass 3 kg moves in a direction making an angle of approximately 22.18 degrees with its original direction of motion.