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# 1) If you drop both a large and a small ball with the large ball beneath the small, then the small ball can bounce higher into the air than if it was...

1) If you drop both a large and a small ball with the large ball beneath the small, then the small ball can
bounce higher into the air than if it was to bounce off the floor directly. If you have a large and small
ball handy you could try it! Assume the mass of the large ball is 0.1 kg and the mass of the small ball is
0.01 kg. The radius of the large ball is 30 cm and the radius of the small ball is 10 cm. The balls are
initially in contact, with the large ball at a height of 1 m (center of the ball). If the balls are released and
fall under gravity to the floor, how high will the small ball bounce up in the air? Assume all collisions
to be elastic.

i. How far do the balls initially fall? How fast are they traveling when the large ball hits the ground?

ii. The large ball can be assumed to hit the floor first and rebound back up. At this point, the large ball
is traveling up and the small ball is traveling down. Both have the same magnitude of velocity found in
i, however, as the collision was “elastic”. Use conservation of momentum in an elastic collision to find
the new velocities of the large and small balls after they collide.

iii. Now the small ball is traveling back up. Given its velocity, how high will it reach?

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