Question

A ball of mass 0.300 kg that is moving with a speed of 7.1 m/s collides head-on and elastically with another ball initially at rest. immediately after the collision, the incoming ball bounces backward with a speed of 3.7 m/s .(a) Calculate the velocity of the target ball after the collision.

Answer 1

To calculate the velocity of the target ball after an elastic collision with an incoming ball, you can use the principles of conservation of momentum and kinetic energy. By setting up and solving equations based on these principles, you can determine the final velocity of the target ball.

Step-by-step explanation:

In this problem, we can use the principles of conservation of momentum and kinetic energy to determine the final velocity of the target ball. Since the collision is head-on and elastic, the momentum and kinetic energy of the system are conserved.

We can start by calculating the initial momentum of the system, which is given by the product of the mass and velocity of the incoming ball: (0.300 kg)(7.1 m/s).

Next, we can set up the equations for conservation of momentum and kinetic energy for the system:

1. Momentum: (0.300 kg)(7.1 m/s) = (0.300 kg)(-3.7 m/s) + (mass of target ball)(final velocity of target ball).
2. Kinetic energy: (1/2)(0.300 kg)(7.1 m/s)^2 = (1/2)(0.300 kg)(-3.7 m/s)^2 + (1/2)(mass of target ball)(final velocity of target ball)^2.

Solving these two equations simultaneously will give us the final velocity of the target ball after the collision.