calculate the probability of collision
Suppose there are 2 circles of radius r, placed at the mid points along the lengths of a rectangle like the picture, What is the probability of collision between the circles before either circle hits a boundary?, the Particles can have any direction, and they must keep the direction until collision. Both particles travel at same speed

- dan815

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- dan815

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- imqwerty

will we consider gravity ?

- ganeshie8

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## More answers

- ganeshie8

I think the locus of intersection points is the perpendicular bisector of the line segment joining those two bubbles

- dan815

yeah we need to consider that mid line only i think too, since this is case where the speed is equal

- dan815

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- ganeshie8

yeah that angle should be same

- dan815

now with in this angle space itself we should find the prob and then see what the total prob is

- dan815

i think we should narrow it down to like how many angle different is possible such that a collision is still possible

- dan815

**how much angle difference**

- dan815

sometimes i m surprised at my own english hehe

- ganeshie8

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- dan815

it doesnt have to be a perfect collision though, it can be off course as long as they touch

- ganeshie8

cant we treat the bubbles as point masses

- ganeshie8

oh they gave radius ok

- dan815

this could be a useful one too like a circle, i think there might be some really neat way to solve this one

- dan815

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- imqwerty

ummm....i am little confused but is this the answer-
probability=L/[2(W+L)]

- dan815

there is some modular form of solution for this problem if u limit the angles these circles can travel to 2pi*k/n , where 0

- dan815

tbh i dont know yet qwerty id have to see your full work

- dan815

here is one way of approaching it

- dan815

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- dan815

now there is a perfect collision for every infinitessimal angle by the proportional gets smaller with some factor

- dan815

as the perfect collision surface area thins out with the angle from the center

- dan815

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- imqwerty

what i did was -
like if we have a system like this -|dw:1441176400369:dw| and we are asked that what is the probability that a ball dropped from above falls in the smaller square....then the probability is - (ar. of small square)/(ar. of big square)
umm wait i think my answer was not correct but can we follow such an approach?

- dan815

ya it is definately something simliar to that

- dan815

the only main thing to consider is how the difference in angle changes

- dan815

as u move above the straight line

- dan815

for imperfect collisions

- ganeshie8

thats really a good idea
for simplicity maybe treat bubbles as point masses first
define two random variables : \(\theta_1, \theta_2\)

- dan815

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- dan815

yah that might actually still be equal if we just use point masses in the end

- ganeshie8

so the probability for perfection collision is \(0\)
because we don't get any area
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