Question

A 100 g ball moving to the right at 4.0 m/s catches up to and collides with a 400 g ball that is moving to the right at 1.0 m/s. If the collision is perfectly elastic, what are the speed and direction of each ball after the collision?

Answer 1

To find the final speed and direction of each ball after an elastic collision, you need to apply the conservation of momentum and the conservation of kinetic energy to solve for the two unknown final velocities.

Step-by-step explanation:

The student asks about the final speed and direction of two balls after a perfectly elastic collision where a 100 g ball moving at 4.0 m/s collides with a 400 g ball moving at 1.0 m/s in the same direction. For perfectly elastic collisions, both momentum and kinetic energy are conserved. We can set up two equations, one for the conservation of momentum and one for the conservation of kinetic energy, and solve them simultaneously to find the final velocities of the two balls.

To solve the problem:

1. Use the conservation of momentum: m1v1_initial + m2v2_initial = m1v1_final + m2v2_final.
2. Use the conservation of kinetic energy: 0.5*m1*v1_initial^2 + 0.5*m2*v2_initial^2 = 0.5*m1*v1_final^2 + 0.5*m2*v2_final^2.
3. Solve the system of equations to find the final velocities, v1_final and v2_final.

After calculations, you will get two possible solutions because it will be a quadratic equation in final velocities. The physically appropriate solution typically would have the lighter mass (in this case, the 100 g ball) moving faster than the heavier mass (the 400 g ball) after the collision, with the direction depending on the difference in their initial velocities and masses.