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## Summary:

- Impact problems involving conservation of momentum and law of restitution help needed please.

The following is from the 2018 AQA AS Further Maths/Mechanics Paper 2 exam:

'Two smooth spheres

(a) Show that the speed of

I have 2 questions regarding this problem:

1) Since momentum is a vector and we don't know the direction of motion of either sphere following collision, how can we form the equation with the correct signs?

2) Newton's experimental law does not involve vectors but I believe I still need to know whether to add or subtract the speeds on separation. Again, since we don't know the direction of either sphere on separation, how do we form this equation with the correct signs?

Thanks for any help.

'Two smooth spheres

*A*and*B*of equal radius are free to move on a smooth horizontal surface. The masses of*A*and*B*are*m*and 4*m*respectively. The coefficient of restitution between the spheres is*e*. The spheres are projected directly towards each other, each with speed*u*, and subsequently collide.(a) Show that the speed of

*B*immediately after the impact with*A*is*u*(3 - 2*e*)/5'I have 2 questions regarding this problem:

1) Since momentum is a vector and we don't know the direction of motion of either sphere following collision, how can we form the equation with the correct signs?

2) Newton's experimental law does not involve vectors but I believe I still need to know whether to add or subtract the speeds on separation. Again, since we don't know the direction of either sphere on separation, how do we form this equation with the correct signs?

Thanks for any help.