1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Time interval btwn 2 particles colliding (each with diff v and elevation)

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Two particles are projected from the same point with velocities v1 and v2 at elevation α1 and α2, respectively, (α1>α2). Show that if they collide in mid-air, interval between firings must be:

    2v1v2sin(α1 - α2)/g(v1cosα1 + v2cosα2)

    2. Relevant equations

    y = xtanα - (1/2)(gx^2)(sec^2(α))/v^2

    t = (vsinα)/g

    3. The attempt at a solution

    since both particles are colliding, they will have the same x,y value, therefore:

    xtanα1 - (1/2)(gx^2)(sec^2(α1))/v1^2 = xtanα2 - (1/2)(gx^2)(sec^2(α2))/v2^2

    xtanα1 - xtanα2 = (1/2)(gx^2)(sec^2(α2))/v2^2 - (1/2)(gx^2)(sec^2(α1))/v1^2

    x(tanα1 - tanα2) = (1/2)(gx^2)[sec^2(α2)/v2^2 -sec^2(α1)/v1^2]

    (tanα1 - tanα2) = (1/2)(gx)[sec^2(α2)/v2^2 -sec^2(α1)/v1^2]

    and with the other equation:

    t1 = (v1sinα1)/g and t2 = (v2sinα2)/g

    t1 - t1 = (v1sinα1)/g - (v2sinα2)/g

    t1 - t1 = (1/g)[v1sinα1 - v2sinα2]

    Now I'm stuck because I'm not sure how to plug one equation into the other... and by the same step eliminate the x from the equation.

    Any clues would be appreciated! Thanks
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted