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A body of mass 1 kg collides head-on elastically with a stationary body of mass 3 kg. After the collision, the 1 kg body reverses its direction and moves with a speed of 2 m/s. What was the initial speed (in m/s) of the 1 kg body before the collision?

1. 2
2. 3
3. 4
4. 6

Correct answer: 4

Solution

Using the elastic collision velocity formula: the velocity of the first body after elastic collision is v1 = (m1-m2)/(m1+m2)*u1. With m1=1, m2=3, and v1 = -2 m/s (reversed, speed 2 m/s): -2 = (1-3)/(1+3)*u1 = -u1/2, so u1 = 4 m/s.

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