Help solve all this question please

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The discussion revolves around a collision problem involving two spheres, P and Q, with different masses and speeds. The key points include finding the post-collision velocities of both spheres in terms of the initial speed and the coefficient of restitution, e. It is established that if sphere P changes direction after the collision, then e must be greater than 1/3. Additionally, the problem requires deriving an expression for the velocity of sphere Q after the collision and demonstrating that the coefficient of restitution between Q and a wall is greater than 1/9 when e is given as 5/9. The coefficient of restitution is defined as the ratio of relative speeds after and before the collision, indicating how elastic the collision is.
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help solve all this question please...:(

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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Do you know any equations that may help?
 
this is the prove question...i don't know wht equation can solve :(
 
Can you define " The coefficient of restitution"?
 

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