Question

In a game of billiards, a red billiard ball is traveling in the positive x-direction with speed v and the cue ball is traveling in the negative x-direction with speed 3v when the two balls collide head on. Which statement is true concerning their velocities subsequent to the collision? Neglect any effects of spin. (a) red ball: 2v; cue ball: 3v (b) red ball: v; cue ball: 2v (c) red ball: 23v; cue ball: v (d) red ball: v; cue ball: 3v (e) The velocities cant be determined without knowing the mass of each ball.

Answer 1

In a head-on collision between two billiard balls A and B, the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Therefore, the statement that is true concerning their velocities subsequent to the collision is option (b) red ball: v; cue ball: 2v.

Step-by-step explanation:

In a head-on collision between two billiard balls A and B, the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Since the red ball is traveling in the positive x-direction with speed v, its momentum is mv (mass times velocity). The cue ball is traveling in the negative x-direction with speed 3v, so its momentum is -3mv.

After the collision, the red ball will have a velocity v, and the cue ball will have a velocity -2v. Therefore, the statement that is true concerning their velocities subsequent to the collision is option (b) red ball: v; cue ball: 2v.

Answer 2

In a game of billiards, the red ball will have a velocity of v and the cue ball will have a velocity of 3v subsequent to their head-on collision.

Step-by-step explanation:

In a game of billiards, when a red billiard ball traveling in the positive x-direction with speed v collides head-on with a cue ball traveling in the negative x-direction with speed 3v, their velocities subsequent to the collision can be determined using the principle of conservation of momentum.

When two objects collide, the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the red ball before the collision is mv, and the momentum of the cue ball before the collision is -3mv (negative because it is moving in the opposite direction).

After the collision, the red ball slows down and moves in the negative x-direction, while the cue ball speeds up and moves in the positive x-direction. The magnitude of their velocities will be different, but the ratio of their velocities will be the same as the ratio of their initial momenta. Therefore, the correct statement concerning their velocities subsequent to the collision is: