Ball A, moving with an initial speed of 3 m/s, has a head-on collision with another ball B at rest, which is twice as massive as A . What are the final velocities of A and B if the collision is elastic?

1 answer

In an elastic collision, both momentum and kinetic energy are conserved.

Conservation of momentum

m*3 = m*vA + 2m*vB
or
3 = vA + 2*VB
where vA is the speed of A, and vB is the speed of B

Conservation of kinetic energy:

1/2*m*3^2 = 1/2*m*vA^2 + 1/2*2*m*vB^2
9 = vA^2 + 2*vB^2

You have two equations with two unknowns:

3 = vA + 2*VB
9 = vA^2 + 2*vB^2

Use algebra to solve for vA and vB