Calculate the momentum vectors before and after collision of particles. Calculate the kinetic energy of the two particles before and after collision.

Trigonometry

Deduce the final equation by using the cos and sin theta

Considerer the collision between a moving particle of mass M1 and an initially stationary particle of mass M2, assume collision occurs at an angle θ defined by the initial trajectory of M1 and the line joining the mass centers at contact.

1- Calculate the momentum vectors before and after collision of particles.

2- Calculate the kinetic energy of the two particles before and after collision.

3- Deduce that the ratio of the kinetic energy (E2) acquired by M2 relative to the kinetic energy (El) of M1 is:

4- Show that for a constant value of θ this ratio is maximum for M1=M2.