Question

Ball B, with a mass of 30kg, is moving to the left at -10 m/s. With what velocity should Ball A, with a mass of 10 kg, move to the right and collide with B, so that Ball A rebounds with a velocity of -30 m/s, and Ball B with velocity of 10 m/s, after the collision? Assume the collision to be perfectly elastic.
Use the formula for perfect elasticity. m1v1(initial) + m2v2(initial) = m1v1(final) + m2v2(final) m1 = mass of object 1, m2 = mass of object 2 v1 = velocity of object 1, v2 = velocity of object 2

Answer 1

Initially, Ball A of 10 kg will have velocity x, while Ball B of 30 kg has velocity -10 m/s.
After collision, Ball A will have a velocity of -30 m/s, while Ball B will have velocity 10 m/s. We assume their masses do not change.
(10 kg)(x m/s) + (30 kg)(-10 m/s) = (10 kg)(-30 m/s) + (30 kg)(10 m/s)
10x - 300 = -300 + 300
x = 30 m/s (to the right)