Question

One pool ball traveling with a velocity of 5m / s hits another ball of the same mass, which is stationary. The collision is head on, as momentum is conserved, and they bounce off each other. What are the final velocities of both bodies?

Answer 1

The final velocity of the first ball is -5 m/s, and the final velocity of the second ball is 5 m/s.

In this scenario, the collision between the two pool balls is elastic, meaning both kinetic energy and momentum are conserved. Initially, the first ball is moving with a velocity of 5 m/s, and the second ball is at rest. Since the collision is head-on, the direction of motion is crucial for determining the signs of the velocities.

Upon collision, the two balls exchange momentum, and according to the conservation of momentum, the total momentum before the collision equals the total momentum after the collision. The momentum of the first ball (m₁v₁) is transferred to the second ball, and vice versa.

If we denote the masses of both balls as m and their initial velocities as u₁ and u₂, and their final velocities as v₁ and v₂, the conservation of momentum equation can be written as:

`m*5=m*v_1 +m*v_2`

​Since the masses cancel out, the equation becomes:

`5=v_1+v_2`

After the collision, the first ball reverses its direction, resulting in a final velocity (v₁) of -5 m/s. The second ball, initially at rest, acquires the momentum of the first ball and moves in the opposite direction, resulting in a final velocity (v₂) of 5 m/s. Thus, the final velocities are -5 m/s for the first ball and 5 m/s for the second ball, satisfying the conservation of momentum and the elastic nature of the collision.