What is the initial speed of the cue ball if it rebounds at 1.00 m/s and hits a stationary ball?

To determine the initial speed of the cue ball, we can analyze the situation using the principles of conservation of momentum and kinetic energy for elastic collisions.

In this scenario, the cue ball strikes a stationary ball (let's call it the target ball), and after the collision, the cue ball rebounds at a speed of 1.00 m/s. If we assume that the cue ball and the target ball have the same mass and that the collision is perfectly elastic, we can use these properties to find the initial speed of the cue ball.

For a perfectly elastic collision involving two objects, the formulas governing the interaction can be set based on the principles that momentum before the collision equals momentum after the collision, and kinetic energy is also conserved. For the cue ball hitting a stationary target ball and rebounding back, the formula is simplified.

In this case, we know that:

• The final speed of the cue ball after the collision is 1.00 m/s (in the opposite direction).

• The target ball starts from rest.

Using the conservation of momentum:

Initial momentum of the cue ball = Final momentum of cue ball + Momentum of the target ball after collision.

Assuming both balls have the same mass (m):

Let ( v ) be