A pool player is attempting a fancy shot.He hits the cue ball giving it a speed of 5.57 m/s and directs its center on a path tangent to the surface of the target ball having the same mass as the cue ball.After the collision (on a frictionless table)the initially-stationary ball moves with a speed of 4.82 m/s.After the collision,the new speed of the cue ball and the relative direction of the balls are closest to
A) 2.79 m/s, at 90° to each other.
B) 2.79 m/s, at 60° to each other.
C) 8.34 m/s, at 90° to each other.
D) 8.34 m/s, at 60° to each other.

Question

Quizplus · Accepted Answer

The conservation of momentum and kinetic energy in elastic collisions applies here. Since the balls have the same mass and the table is frictionless, the velocities can be calculated using these principles. The speed of the cue ball after the collision can be found using the conservation of momentum and the fact that the collision is elastic. The direction at 90° indicates that the collision was perfectly elastic and the balls had equal masses, which is a characteristic outcome for such collisions when one ball strikes another at a tangent.

A Pool Player Is Attempting a Fancy Shot