Question

If a ping pong ball and a golf ball are both moving in the same direction with the same amount of kinetic energy, the speed of the ping pong ball must be
A. less than golf ball
B. same as golf ball
C. more than golf ball
D. impossible to know

Answer 1

If the kinetic energy of each ball is equal to that of the other,
then

(1/2) (mass of ppb) (speed of ppb)² = (1/2) (mass of gb) (speed of gb)²

Multiply each side by 2:

      (mass of ppb) (speed of ppb)² = (mass of gb) (speed of gb)²

Divide each side by (mass of gb) and by (speed of ppb)² :

     (mass of ppb)/(mass of gb)  =  (speed of gb)²/(speed of ppb)²

Take square root of each side:

       √ (ratio of their masses)  =  ( 1 / ratio of their speeds)²

By trying to do this perfectly rigorously and elegantly, I'm also
using up a lot of space and guaranteeing that nobody will be
able to follow what I have written.  Let's just come in from the
cold, and say it the clear, easy way:

If their kinetic energies are equal, then the product of each
mass and its speed² must be the same number.

If one ball has less mass than the other one, then the speed²
of the lighter one must be greater than the speed² of the heavier
one, in order to keep the products equal.

The pingpong ball is moving faster than the golf ball.

The directions of their motions are irrelevant.