Probability of puck bouncing of wald

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In summary, there is a rectangular surface with no friction and a puck with no friction on its bottom surface. The puck is given a push in a random direction and will continue to bounce off the walls at the same speed due to the coefficient of restitution of 1. The probability of the puck eventually passing through the same point, moving in the same direction, is 100%. However, if dealing with a continuum, a probability density is needed, taking into account the probability per unit area of occupying a point and the probability per unit angle of having the given velocity.
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There is a rectangular surface with no friction, and a puck with no friction on its bottom surface sits at a random point on this surface. This puck is now given a push in a random direction. The walls of the surface all have coefficient of restitution of 1, so the puck will bounce off the walls forever at the same speed.

What is the probability that the puck will eventually pass through the same point, moving in the same direction ?
 
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100% -
 
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If you are dealing with a continuum, you need a probability density. That is, probability per unit area of occupying a point, and probability per unit angle of having the given velocity.
 

FAQ: Probability of puck bouncing of wald

What is the probability of a puck bouncing off a wall?

The probability of a puck bouncing off a wall depends on several factors, such as the material and surface of the wall, the angle at which the puck hits the wall, and the speed and direction of the puck. It is difficult to determine a specific probability without knowing these variables.

How can the probability of a puck bouncing off a wall be calculated?

The probability of a puck bouncing off a wall can be calculated using mathematical equations and principles of physics, such as the laws of motion and conservation of energy. It also requires knowledge of the variables mentioned in the previous answer.

Does the shape of the wall affect the probability of a puck bouncing off it?

Yes, the shape of the wall can affect the probability of a puck bouncing off it. For example, a flat and smooth wall may have a higher probability of a puck bouncing off it compared to a curved or rough wall. This is because the surface of the wall can affect the angle and speed at which the puck bounces.

Is there a way to increase the probability of a puck bouncing off a wall?

Yes, there are certain techniques that can be used to increase the probability of a puck bouncing off a wall. These include adjusting the angle and speed at which the puck is shot, using a material with a higher coefficient of restitution for the wall, and creating a surface texture that promotes bouncing.

Can the probability of a puck bouncing off a wall be predicted with 100% accuracy?

No, it is not possible to predict the probability of a puck bouncing off a wall with 100% accuracy. This is because there are many variables that can affect the outcome, and it is impossible to account for all of them. However, with precise measurements and calculations, it is possible to make a fairly accurate prediction.

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