What are the final velocities of each ball in a perfectly elastic collision?

Question

Ball 1, with a mass of 80 g and traveling at 14 m/s, collides head on with ball 2, which has a mass of 280 g and is initially at rest.

What are the final velocities of each ball if the collision is perfectly elastic?

Answer 1

In general the relationship you are seeking is the law of conservation of momentum.  In this case we are talking about elastic collisions which conserve kinetic energy as well as total momentum before and after collision.  Since this is a head-on collision (one dimensional) the math is not too difficult.  From the Wikipedia page cited below we get the following relationships:

m1*v1f + m2*v2f = m1*v1i + m2*v2i  (conserv momentum)

m1*v1f^2 + m2*v2f^2 = m1*v1i^2 + m2*v2i^2 (conserv kinetic energy)

m1=80g, m2=280g, v1i=14m/s, v2i=0m/s. Two equations with two unknowns; use simultaneous equations to get the answer.

PS.  The '^' symbol in the equations means 'to the power of'.  The 'i' suffix represents the initial state whereas the 'f' suffix represents the final state.