Elastic collisions in two dimensions: 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

Question

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved. Given that the balls have the same mass and the target ball moves with a speed of 4.82 m/s after the collision, the cue ball must slow down due to the conservation of momentum. The conservation of kinetic energy and momentum in such collisions, especially when one object is initially stationary and the objects have equal mass, results in the two objects moving perpendicular to each other if they have different final speeds. The speed of the cue ball can be found using the conservation of energy and momentum, leading to a decrease in its speed and a perpendicular motion relative to the target ball.

Elastic Collisions in Two Dimensions: a Pool Player Is Attempting