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Math Help - Projectiles Question

  1. #1
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    Unhappy Projectiles Question

    A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

    a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

    b) Find the height above the ground at which this occurs

    If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.
    Last edited by mr fantastic; July 30th 2010 at 11:12 PM. Reason: Deleted useless phrase from post.
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    Quote Originally Posted by Tilleard View Post
    A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

    a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

    b) Find the height above the ground at which this occurs

    If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.
    Is it to be assumed that air resistance is negligible?
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  3. #3
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    Quote Originally Posted by Tilleard View Post
    A particle of mass m is projected vertically upwards with speed u and when it reaches its greatest height a second particle of mass 2m is projected vertically upward with speed 2u from the same point as the first.

    a) Prove that the time that elapses between the projection of the second particle and the collision with the first is u/4g

    b) Find the height above the ground at which this occurs

    If on collision the particles coalesce prove that the combined particle will reach a greatest height of 19U power 2 / 18g above the point of projection.
    First find the greatest height of the first particle.

    Take the time of greatest height (call this height h_{max}) of the first particle as 0. Now the problem (a) is that of finding the time of collision of an upward projected particle from h=0 with initial speed of 2u and one falling from rest from h_{max}

    CB
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