A ball at rest is hit by a ball of the same weight coming down a ramp. The balls collide and both fall to the floor in different directions.  The same scenario above happens but the ball at rest is lighter than the ball coming down the ramp.  Why must the displacement vector of the lighter ball be scaled by the ratio of masses of the two balls?

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A ball at rest is hit by a ball of the same weight coming down a ramp. The balls collide and both fall to the floor in different directions. 

The same scenario above happens but the ball at rest is lighter than the ball coming down the ramp. 

Why must the displacement vector of the lighter ball be scaled by the ratio of masses of the two balls?

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