Billiard collision with same angle

In summary, Jeanette needs to sink the 9-ball from the final rack in order to win the 9-ball pool tournament. She must carefully line up her shot to ensure that the cue ball and the 9-ball move away from each other at the same angle from the direction of the cue ball's initial speed. The collision is assumed to be perfectly elastic, with no friction or spinning of the balls. To solve this problem, one must use conservation of momentum in the x and y directions and conservation of energy.
  • #1
madman143
11
0

Homework Statement



Jeanette is playing in a 9-ball pool tournament. She will win if she sinks the 9-ball from the final rack, so she needs to line up her shot precisely. Both the cue ball and the 9-ball have mass , and the cue ball is hit at an initial speed of . Jeanette carefully hits the cue ball into the 9-ball off center, so that when the balls collide, they move away from each other at the same angle from the direction in which the cue ball was originally traveling (see figure). Furthermore, after the collision, the cue ball moves away at speed , while the 9-ball moves at speed . (Intro 1 figure)

For the purposes of this problem, assume that the collision is perfectly elastic, neglect friction, and ignore the spinning of the balls.

pic attached

Homework Equations


v final=v

i get theta=cos^-1(v intial/2v)

please help. no numericals were given in this problem?
 

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  • #2
First of all figures that Jeanette would choke on the money ball. But that said, don't you also need to conserve kinetic energy as well?
 
  • #3
you've got conservation of momentum along the x direction and along the y direction, see if you can throw those two equations down, then throw down one more with conservation of energy.
 

1. What is a billiard collision with same angle?

A billiard collision with same angle refers to the scenario where two billiard balls collide at the same angle, resulting in both balls moving in the same direction.

2. What happens to the energy of the billiard balls in this type of collision?

In a billiard collision with same angle, the energy of the billiard balls remains the same. This is due to the conservation of energy principle, where energy cannot be created or destroyed, but can only be transferred from one form to another.

3. How does the mass of the billiard balls affect the collision?

The mass of the billiard balls does not affect the collision in terms of the angle at which they will move. However, the heavier ball will transfer more force to the lighter ball, causing it to move faster.

4. Are there any real-life applications of this type of collision?

Yes, this type of collision is commonly seen in sports such as pool and billiards, where players use the angles of collisions to strategically move the balls around the table.

5. Is the angle of collision the only factor that determines the direction of the balls?

No, the angle of collision is not the only factor that determines the direction of the balls. Other factors such as the speed, mass, and spin of the balls also play a role in the final direction of the balls after the collision.

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