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# help with maths question M2 watch

1. 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!
2. (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?
3. Im countering some difficulty starting from part b. Do you know how to solve the question?
4. (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?
5. -v

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