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`        Consider the given table: a ball is fired from one of the foci with a velocity of 5m/s, at an angle 30* with the major axis of the elliptical table.The question:When does it again return to the same point as which it was fired from, for the very first time??? (does it ever).Assume the major axis of the ellipse to be 10 meters, and its eccentricity is .8.Assume all collisions to be completely elastic.                                                                                                                                                                                                                                                                                 THE DIAGRAM IS IN THE LINK         http://2.bp.blogspot.com/_PG0ockp6BCI/S5uVjFcEggI/AAAAAAAAAEs/nzbiBktiwwI/s1600-h/illuminati.jpg`
7 years ago

Chetan Mandayam Nayakar
312 Points
```										after the first collision, the ball reaches the other focus after travelling 10m @5m/s. therefore, time for first trip=2seconds.
it takes another 2seconds to reach the point from which it was fired. thus, total time for first return=4seconds.
the length of each trip is is equal to the major axis because, an ellipse is the locus of a point which moves such that the sum of its distances from 2 different points is constant. this constant is the length of the major axis. the ball goes from one focus to the other if the collisions are elastic because of the mathematical properties of the ellipse
```
7 years ago
Chetan Mandayam Nayakar
312 Points
```										It can be shown that in the case of an ellipse, if from any point on the boundary, lines are drawn passing through the foci, the normal to the ellipse at that point bisects the angle between the two lines. Therefore, because the collisions are perfectly elastic, the ball will hit the boundary once, go through the other focus, again hit the boundary and return to the starting point.
Now, an ellipse can also be defined as the locus of a point which moves such that the sum of its distances from two points(foci) is a constant(major axis) '2a'. Time taken=2*10/5=4sec
```
6 years ago
Chetan Mandayam Nayakar
312 Points
```										An ellipse is also defineable as the locus of a point which moves such that the sum of its distances from two points(foci) is a constant(=2a, the major axis). Also, in an ellipse the normal at any point bisects the angle between the lines from the two foci to the point. And the collisions are perfectly elastic. Therefore, the ellipse will collide once with the boundary, passes through the other focus, once again collides with the boundary and returns to the starting point.
distance covered= 2*10=20m,speed=5m/s,time=20/5=4sec
```
6 years ago
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