# What is the speed of the 8-ball after the collision?

• Whitestripes
In summary, the conversation discusses a pool game where the cue ball collides with the 8-ball, resulting in the 8-ball moving at an angle theta with respect to the original direction of the cue ball. The pool table is assumed to be frictionless and the masses of both balls are equal. The relevant equations for this scenario include conservation of momentum and energy, and the velocity of the 8-ball can be determined without knowing the velocity of the cue ball.
Whitestripes

1. In a pool game, the cue ball, which has an initial speed of 1.3 m/s, makes an elastic collision with the 8-ball, which is initially at rest. After the collision, the 8-ball moves at an angle theta = 33.2o with respect to the original direction of the cue ball, as shown in the figure. Assume the pool table is frictionless and the masses of the cue ball and the 8-ball are equal. What is the speed of the 8-ball after the collision?

2. Mgh + W = 1/2mv^2
p=mv
3. I was easily able to get that phi was 56.8 deg because of the 90 deg angle. Now I am lost at how to find the velocity of the 8 ball without the velocity of the cue ball?

Hello White and welcome to PF :-)

Your collection of relevant equations needs revision and extension. Mgh and W are unlikely to play a role in this drama...

Conservation of momentum and energy are most important. But "Mgh" is irrelevant here. It is the potential energy of a mass M at height h, but there is no "height" here.

## What is the speed of the 8-ball after the collision?

The speed of the 8-ball after the collision depends on various factors, including the initial speed of the cue ball, the angle of impact, and the friction of the table surface.

## How is the speed of the 8-ball calculated after the collision?

The speed of the 8-ball after the collision can be calculated using the principles of conservation of momentum and energy. This involves considering the masses and velocities of both the cue ball and the 8-ball before and after the collision.

## Does the speed of the 8-ball change after multiple collisions?

Yes, the speed of the 8-ball can change after multiple collisions. Each collision involves a transfer of energy and momentum, which can affect the speed and direction of the 8-ball.

## How does the speed of the 8-ball affect its trajectory after the collision?

The speed of the 8-ball can affect its trajectory after the collision. A higher speed can result in a longer and straighter path, while a lower speed can cause the ball to curve or bounce off other balls or the walls of the table.

## Can the speed of the 8-ball be accurately predicted before the collision?

The speed of the 8-ball cannot be accurately predicted before the collision as it depends on various factors and can change during the collision itself. However, it can be estimated using mathematical equations and physical principles.

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