Solving a Ball Bouncing in Stairs: Need Help?

[mpthimios]

I do not know if my problem is advanced, but in any case I place it here
Well this it :
A ball bounces in the stairs of a staircase. Let l=-(Vfk/Vik) where Vfk the velocity just before the colision with a stair and Vik the velocity just after.
the height and the Length of the stairs is L (the same).
The ball always reaches he same height H (from the stair). The ball always travels the same distance X between two coisions with the stares.
I want to find the H and Vx using L and l only (H = f (L,l), Vx = f (L,l)).
Any help?
The shape is not so good but I hope you understand the concept..

 

[Jhero]

Hello,

Thank you for sharing your problem with us. It seems like a interesting and challenging one. Based on the given information, it is possible to find the height and horizontal velocity of the ball using the length and the coefficient of restitution, l. However, it would be helpful to have more information such as the mass and initial velocity of the ball, as well as the number of stairs in the staircase. These factors can affect the calculations and provide more accurate results.

In general, the height of the ball can be calculated using the formula H = (l^n)L, where n is the number of stairs. The horizontal velocity, Vx, can be found using the equation Vx = (2l^n)L/T, where T is the time taken for the ball to reach the same height H again.

I would recommend conducting an experiment to gather more data and validate the calculations. This can also help in determining the relationship between the variables and provide a more comprehensive understanding of the problem. Additionally, considering the elasticity of the stairs and the ball can also impact the results.

I hope this helps and I wish you the best of luck in finding a solution to your problem. Do let us know if you have any further questions or updates on your findings. Thank you.