Question

that the collision is inelastic, and that both balls have the same mass, at what angle will the cue ball be deflected?Below the ball's initial direction Above the ball's initial direction Tries 0/1 What will be the speed of the cue ball?

Answer 1

To find the final velocity of the cue ball in an inelastic collision at a given angle, the principles of conservation of momentum and conservation of kinetic energy can be used. The final velocity can be determined by setting the initial momentum of the system equal to the final momentum and using the information that the cue ball loses 20% of its original speed. The final velocity can then be calculated using the equation for conservation of kinetic energy, considering that the final kinetic energy is 80% of the initial kinetic energy.

Step-by-step explanation:

In an inelastic collision, both balls stick together after colliding. The final velocity of the cue ball depends on the initial velocities of both balls and the angle at which they collide. Let's assume the cue ball is initially traveling in the x-direction and the second ball is initially traveling at an angle of θ to the x-axis.

To find the final velocity of the cue ball, you can use the principles of conservation of momentum and conservation of kinetic energy. The momentum in the x-direction will be conserved, so you can set the initial momentum of the system equal to the final momentum:

1. m1v1i + m2v2i = (m1 + m2)vf
2. The kinetic energy will not be conserved because the collision is inelastic, so we can't set the initial kinetic energy equal to the final kinetic energy. Instead, we can use the given information that the cue ball loses 20% of its original speed to find the final velocity of the cue ball. The initial kinetic energy of the system is:
3. KEinitial = ½m1(v1i)2 + ½m2(v2i)2
4. And the final kinetic energy is:
5. KEfinal = ½(m1 + m2)vf2
6. We can then use the information that the final kinetic energy is 80% of the initial kinetic energy to solve for the final velocity of the cue ball.