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    A uniform smooth sphere P,of mass 3m, is moving in a straight line with speed u on a smooth horizontal table.Another uniform smooth sphere Q, of mass and m and having the same radius as P, moving with speed 2u in the same straight line as P but in the opposite direction to P. The sphere P collides with the sphere Q directly. The velocities of P and Q after the collision are v and w respectively, measured in the direction of motion of P before the collision. The coefficient of restitution between P and Q is e.
    a) Find an expression for v in terms of u and e.
    b) Show that, if the direction of motion and P is changed by the collision, then e>1/3.
    c) Find an expression for w in terms of u and e.
    Following the collision with P, the sphere Q then collides with and rebounds from a vertical wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between Q and the wall is e' Given that e=5/9, and that P and Q collide again in the subsequent motion,
    e) Show that e'>1/9.

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    (Original post by ajhye.98)
    A uniform smooth sphere P,of mass 3m, is moving in a straight line with speed u on a smooth horizontal table.Another uniform smooth sphere Q, of mass and m and having the same radius as P, moving with speed 2u in the same straight line as P but in the opposite direction to P. The sphere P collides with the sphere Q directly. The velocities of P and Q after the collision are v and w respectively, measured in the direction of motion of P before the collision. The coefficient of restitution between P and Q is e.
    a) Find an expression for v in terms of u and e.
    b) Show that, if the direction of motion and P is changed by the collision, then e>1/3.
    c) Find an expression for w in terms of u and e.
    Following the collision with P, the sphere Q then collides with and rebounds from a vertical wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between Q and the wall is e' Given that e=5/9, and that P and Q collide again in the subsequent motion,
    e) Show that e'>1/9.

    Thank you!
    Hi. I have solved the whole question and would be happy to help you through it. Which part are you having trouble with in particular?
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    Im countering some difficulty starting from part b. Do you know how to solve the question?
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    (Original post by ajhye.98)
    Im countering some difficulty starting from part b. Do you know how to solve the question?
    Yeah. Here is a hint:

    If the direction of motion of P is changed, what can you say about v?
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