First time i had to use this forum in a long time but im very stuck today and cant find a way out of it after over an hour and with reading my notes so here goes.

1)a proton of mass m travelling at 300m/s collides with a stationary carbon nucleus of mass 12m, the collision is elastic and head-on.

(a)

**find the velocity of the centre of mass of the system**, for this i took an imaginary particle of mass 13m and used conservation of momentum to find a velocity of 23.07m/s ....not sure if that is right

(b)

**find the velocity of the proton after the collision in the centre of mass reference frame**ive tried playing around with conservation of momentum for a while and with conservation of kinetic energy but my answer seems to always come out at either 0 or 300, not got a clue what im doing wrong

(c)

**find the velocity of the proton after the collision in the lab reference frame**i really am stuck on how to do this with conservation of momentum giving me one equation but 2 un-knowns

2)

**a bullet of mass m1 is fired with a speed v into the bob of a ballistic pendulum of mass m2. find the maximum height h attained by the bob if the bullet passes through the bob and emerges with a speed v/2**unfortunately i was hungover during this lecture and ended up falling asleep...... whoooops, but it was a birthday night before so how could i not?

if anyone could point me in the right direction with these it would be greately appreciated

thanks