# Odd quetsion about elastical collision

1. Dec 26, 2008

### KFC

1. The problem statement, all variables and given/known data
One particle with mass m is sitting at rest at the original of the rectangular coordinate system. Another particle, with mass M, is moving along x axis and hit m at the original. Assume the collision is complete elastic so that M move along the direction making an angle A with positive x-axis, while m move along other direction making angle B with positive x-axis. We only know that after collision, M's momentum is 1/k of original momentum (0 < 1/k < 1). Try to find out over what range of m/M is this possible.

2. The attempt at a solution
Assume the initial momentum of the system is P0, since M's final momentum becomes P0/k, so mass m will attain momentum (k-1)P0/k. Due to conservation of momentum, we have

$$P_0 = \frac{P_0}{k}\cos A + \frac{(k-1)P_0}{k}\cos B$$

along the vertical direciton, momentum also conserved

$$\frac{P_0}{k}\sin A = \frac{(k-1)P_0}{k}\sin B$$

These two equations are enough to solve for angle A and B so that we can find the relation between ratio of mass and ratio of velocity. But since we have a definite solution of A and B, why the question asking for a range of ration of mass make it possible? I have no idea how to do that.