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dan815
 one year ago
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
 one year ago
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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imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2will we consider gravity ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441175324916:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I think the locus of intersection points is the perpendicular bisector of the line segment joining those two bubbles

dan815
 one year ago
Best ResponseYou've already chosen the best response.3yeah we need to consider that mid line only i think too, since this is case where the speed is equal

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yeah that angle should be same

dan815
 one year ago
Best ResponseYou've already chosen the best response.3now with in this angle space itself we should find the prob and then see what the total prob is

dan815
 one year ago
Best ResponseYou've already chosen the best response.3i think we should narrow it down to like how many angle different is possible such that a collision is still possible

dan815
 one year ago
Best ResponseYou've already chosen the best response.3**how much angle difference**

dan815
 one year ago
Best ResponseYou've already chosen the best response.3sometimes i m surprised at my own english hehe

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441175544779:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.3it doesnt have to be a perfect collision though, it can be off course as long as they touch

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1cant we treat the bubbles as point masses

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1oh they gave radius ok

dan815
 one year ago
Best ResponseYou've already chosen the best response.3this could be a useful one too like a circle, i think there might be some really neat way to solve this one

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2ummm....i am little confused but is this the answer probability=L/[2(W+L)]

dan815
 one year ago
Best ResponseYou've already chosen the best response.3there is some modular form of solution for this problem if u limit the angles these circles can travel to 2pi*k/n , where 0<k<n, and k,n are integers then you can consider the cases where boundary collision is taken into account and see when the first collision occurs vs another circle, this problem looks very similiar to modular arithmetic problems

dan815
 one year ago
Best ResponseYou've already chosen the best response.3tbh i dont know yet qwerty id have to see your full work

dan815
 one year ago
Best ResponseYou've already chosen the best response.3here is one way of approaching it

dan815
 one year ago
Best ResponseYou've already chosen the best response.3now there is a perfect collision for every infinitessimal angle by the proportional gets smaller with some factor

dan815
 one year ago
Best ResponseYou've already chosen the best response.3as the perfect collision surface area thins out with the angle from the center

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2what 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
 one year ago
Best ResponseYou've already chosen the best response.3ya it is definately something simliar to that

dan815
 one year ago
Best ResponseYou've already chosen the best response.3the only main thing to consider is how the difference in angle changes

dan815
 one year ago
Best ResponseYou've already chosen the best response.3as u move above the straight line

dan815
 one year ago
Best ResponseYou've already chosen the best response.3for imperfect collisions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1thats really a good idea for simplicity maybe treat bubbles as point masses first define two random variables : \(\theta_1, \theta_2\)

dan815
 one year ago
Best ResponseYou've already chosen the best response.3yah that might actually still be equal if we just use point masses in the end

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so the probability for perfection collision is \(0\) because we don't get any area dw:1441177185300:dw