- #1

CherryWine

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## Homework Statement

A ball is rolling towards a rectangular hole which is 40cm deep and 2cm wide with a velocity 1m/s. It falls through the hole, bounces off the walls a couple of times and falls down. The direction of balls motion is perpendicular to the hole (falling in it from one side). Diameter of the ball is 0.6cm. How many times will the ball bounce off the walls until reaching the bottom? Suppose ideal elastic collisions with the walls of the hole that last for negligible time.

## Homework Equations

All 2D equations.

## The Attempt at a Solution

I solved the problem by using series. Firstly, using y(t) equation for 2D, I found expressions for y after one, two and three bounces from the walls. Then I checked for a pattern and saw that the general term for y is (n-1/2)*gt^2. Then I formed a series ∑(n-1/2)*gt^2 (n going from 1 to i, where i is the number of bounces needed) and then equated that series with 0,4 m which is the height of the hole. By trial and error I found the correct answer which is i=20 (the ball bounces 20 times), but I would like to know some other method because I doubt that this problem should have been solved by using series. And finally, in the series I found i by trial and error with a calculator, but I am also interested in a purely mathematical method that would give me that i. Also I found t, by using this equation D-d=V*t, where D is the width of the hole and d is the diameter of the ball, t is equal to 0,014s, that is the time needed for one bounce, and it is constant.