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Homework Statement
This question is actually two question. We have two hollow frames  one is rectangular and another is triangular. the rectangle is rotated and fixated such that the angles in shape are ##\alpha , \beta = 90  \alpha## and the angle of triangle is ##\alpha##. We have two balls in each frame like the picture and we release them at the same time and when one gets to one end (except destination) it will continue its path with the same velocity magnitude and new direction so the velocity is never zero except for the start.
We want to find which ball gets to destination first. (Each frame is a different question and they are not related)
There is NO friction or air resistance but there is gravity (##g \approx 9.8 m/s^2##). Also the Thickness of frames are small and equal on each side and balls completely fit in the frame. The pictures are exaggerated. So no calculations needed for the Thickness. They both start with ##v = 0##.
The Attempt at a Solution
I tried to solve the triangle one, after finding speeds at end of the vertical path and solving the equations, and a lot of factorization and cancelling common terms out, I get something like ##cos \alpha / \sqrt{2 sin \alpha} + \sqrt{2 sin \alpha}## Compared to ## \sqrt{2 /sin \alpha}##. For the rectangular one, it gets a lot more complex. I want to know does it really depend to ##\alpha## and ##\beta##?
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