Question

A billiard ball traveling at (2.2m/s)^i−(0.4m/s)ʲ collides with a wall that is aligned in the ʲ direction. Assuming the collision is elastic, what is the final velocity of the ball?

a) (2.2m/s)^i −(0.4m/s)ʲ
b) (2.2m/s)^i+(0.4m/s)ʲ
c) (2.2m/s)^i−(0.4m/s)ʲ reflected along the j-axis
d) (2.2m/s)^i+(0.4m/s)ʲ reflected along the j-axis

Answer 1

The final velocity of a billiard ball in an elastic collision with a wall aligned in the Ĵ direction is (2.2 m/s) Î + (0.4 m/s) Ĵ, as the horizontal velocity remains the same while the vertical component reverses.

Step-by-step explanation:

When a billiard ball traveling at (2.2 m/s) Î - (0.4 m/s) Ĵ collides with a wall that is aligned in the Ĵ direction and the collision is elastic, the final velocity of the ball can be determined by looking at the behavior of each component of the velocity.

An elastic collision is one where there is no loss in kinetic energy, and typically, the only change would be the direction of the velocity component that is perpendicular to the surface of the wall. Therefore, the horizontal (i) component remains unchanged, and the vertical (j) component would reverse in direction.

Considering this, the final velocity would be (2.2 m/s) Î + (0.4 m/s) Ĵ, because the horizontal component stays the same, but the vertical component (originally in the negative Ĵ direction) now flips to be in the positive Ĵ direction after the elastic collision with the wall aligned in the Ĵ direction.