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

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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

Mathematics
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|dw:1441174469829:dw|
will we consider gravity ?
|dw:1441175324916:dw|

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I think the locus of intersection points is the perpendicular bisector of the line segment joining those two bubbles
yeah we need to consider that mid line only i think too, since this is case where the speed is equal
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yeah that angle should be same
now with in this angle space itself we should find the prob and then see what the total prob is
i think we should narrow it down to like how many angle different is possible such that a collision is still possible
**how much angle difference**
sometimes i m surprised at my own english hehe
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it doesnt have to be a perfect collision though, it can be off course as long as they touch
cant we treat the bubbles as point masses
oh they gave radius ok
this could be a useful one too like a circle, i think there might be some really neat way to solve this one
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ummm....i am little confused but is this the answer- probability=L/[2(W+L)]
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
tbh i dont know yet qwerty id have to see your full work
here is one way of approaching it
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now there is a perfect collision for every infinitessimal angle by the proportional gets smaller with some factor
as the perfect collision surface area thins out with the angle from the center
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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?
ya it is definately something simliar to that
the only main thing to consider is how the difference in angle changes
as u move above the straight line
for imperfect collisions
thats really a good idea for simplicity maybe treat bubbles as point masses first define two random variables : \(\theta_1, \theta_2\)
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yah that might actually still be equal if we just use point masses in the end
so the probability for perfection collision is \(0\) because we don't get any area |dw:1441177185300:dw|