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posted by Bertrand .
A 10 kg ball traveling at 5 m/s [S20E] has an elastic collision with a 15 kg ball traveling at 3 m/s [N50W]. If the first ball leaves the collision at 2 m/s [S40W] what is the second ball's velocity?

Since it is an elastic collision, total kinetic energy is conserved. They give you enough information to compute the initial kinetic energy of both balls and the final kinetic energy of the 10 kg ball. You don't need all the data about directions to solve for the 15 kg ball's final velocity.
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