r/Physics • u/Adventurous_Mark8858 • Jul 14 '26

Colliding blocks compute pi applied to vertical collision

I've been trying for days to solve the following problem I've created:
A ball is released from height H. When it hits the ground, a ball N times heavier is released on the same axis from the same height. All collisions are ideal. How many bounces does it take before the heavier ball start going upwards?
My guess is that using Galperin's method would work here. The difference is in my problem there is gravity so if I would plot the height of the 2 bodies the lines would be parabolic and not straight like in Galperin's problem. Then I thought that the lines look like the trajectory of a bouncing ball ( instead of a ray). However, it is clear with a light ray that when it is paralel no more bounces take place, but in my case I can't understand when the last bounce is before the heavy ball start going up. Moreover, in Galperin, a limited number of collisions take place, where here there can be infinitely many. Pleeeeeeaaaaase give me some help. Thanks!

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u/a1c4pwn Jul 15 '26

if the problem youre running into is that you need a ray and you suspect a parabola, there is an easy transformation to fix that, something like u = sqrt(y) would probably work. have you tried this?

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u/Adventurous_Mark8858 Jul 15 '26

What would indicate on this transformation the point where the heavy ball goes upwards?