Question

A ball with a mass of 0.1 kg is traveling with a velocity of 0.5 m/s in the positive x-direction and collides head-on with a 5 kg ball that was at rest. Assuming that it is elastic, find the velocities in m/s) of the balls after the collision.

Answer 1

In an elastic collision between two objects of equal mass where mass A is initially moving with a velocity of 5.0 m/s in the +x-direction and mass B is initially moving with a velocity of 3.0 m/s in the -x-direction, the velocity of mass B after the collision is 3.0 m/s in the +x-direction.

Step-by-step explanation:

In an elastic collision between two objects of equal mass, the total momentum and kinetic energy of the system is conserved. In this case, mass A is initially moving in the +x-direction with a velocity of 5.0 m/s, while mass B is initially moving in the -x-direction with a velocity of 3.0 m/s. After the collision, if mass A moves with a velocity of 3.0 m/s in the -x-direction, we can determine the velocity of mass B using the principle of conservation of momentum.

To find the velocity of mass B, we can use the equation:

massA * velocityA, initial + massB * velocityB, initial = massA * velocityA, final + massB * velocityB, final

Substituting the given values, we have:

massA * 5.0 m/s + massB * (-3.0 m/s) = massA * (-3.0 m/s) + massB * velocityB, final

Solving for velocityB, final, we find that the velocity of mass B after the collision is 3.0 m/s in the +x-direction.