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A 20 gram ball (m_1) elastically collides with a 50 gram ball (m_2) which was initially...

A 20 gram ball (m_1) elastically collides with a 50 gram ball (m_2) which was initially at rest. After the balls collide, m_1 moves backwards at 0.5 m/s.
a) What is the initial velocity of m_1?
b) What is the final velocity of m_2?
c) How do you prove mathmatically that the kinematic energy was preserved?

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