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but i have 2 problems that i have been playing with for over an hour now and just cannot get any kind of reasonable answer

1) a proton of mass m travelling at 300m/s collides with a stationary carbon nucleus of mass 12m

(a) find the velocity of the centre of mass of the system, for this i got 23.07m/s not sure if this is right or wrong, i simply used conservation of momentum for an imaginary particle of mass 13m

(b) find the velocity of the proton after the collision in the centre-of-mass refrence frame (very lost on this)

(c) find the velocity of the proton after the collision in the lab reference frame, for this i have used conservation of momentum, but with 2 un-knowns and only 1 equation i was thinkin of possibly using the conservation of kinetic energy (with it being an elastic collision) but it didnt work out when i tried

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 heigh h attained by the bob if the bullet passes through the bob and emerges with a speed v/2

to be honest this is the lecture i was hungover in and do not have a clue on this one

if someone could point me in the right direction on these it would be grately appreciated

thanks :)