A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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

  • This Question is Closed
  1. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441174469829:dw|

  2. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    will we consider gravity ?

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1441175324916:dw|

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  5. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  6. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441175465518:dw|

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah that angle should be same

  8. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  9. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  10. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    **how much angle difference**

  11. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sometimes i m surprised at my own english hehe

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1441175544779:dw|

  13. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cant we treat the bubbles as point masses

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh they gave radius ok

  16. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  17. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441175998926:dw|

  18. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  19. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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<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

  20. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  21. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    here is one way of approaching it

  22. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441176643347:dw|

  23. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  24. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  25. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441176750326:dw|

  26. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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?

  27. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ya it is definately something simliar to that

  28. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  29. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    as u move above the straight line

  30. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    for imperfect collisions

  31. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  32. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441176897902:dw|

  33. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

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

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so the probability for perfection collision is \(0\) because we don't get any area |dw:1441177185300:dw|