Ball 1 of mass m travels at a velocity of v m/s south and collides with Ball 2 of mass 3m which is travelling at a velocity of v/2 north. If the final velocity of ball 1 is v/4 north, what is the final velocity of ball 2

2/3v m/s

Explanation:

Given that

Mass of ball 1 = m

Initial velocity u1 of ball 1 = v m/s

Mass of ball 2 = 3m

Initial velocity u2 of ball 2 = v/2 m/s

Final velocity v1 of ball 1 = v/4 m/s

Final velocity v2 of ball 2 = ?

To solve this question, we will be applying the law of conservation of momentum, which is mathematically given as

m1u1 + m2u2 = m1v1 + m2v2

If we substitute the given values directly, we have

m * v + 3m * v/2 = m * v/2 + 3m * v2

mv + 3mv/2 = mv/2 + 3m * v2, collecting like terms, we have

mv + 3mv/2 - mv/2 = 3m * v2

mv + 2mv/2 = 3m * v2

mv + mv = 3m * v2

2mv = 3m * v2, dividing both sides by 3m

v2 = 2mv/3m

v2 = 2/3v

Therefore, the final velocity v2 of ball 2 is 2/3v

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