1. The problem statement, all variables and given/known data I have two particles moving on a smooth horizontal table. The first, A, has mass m and the second, B, has mass 3m. A has velocity 2i + 3j and B has velocity 6i - 5j. They collide at the origin at t=0 and coalesce. I have to 1) determine the velocity of the coalesced particle after the collision; 2) determine the amount of energy lost in the collision; 3) find expressions for rA(t) and rB(t) at time t<0; 4) find the position vector of the centre of mass of the system before the collision; 5) determine the velocity of the centre of mass; 6) find the position vector of the coalesced particles at time t>0 after the collision; and 7) comment on the answers to parts 3)-6) 2. Relevant equations I've used the following: 1) Total linear momentum of system P=mv and found P of A is 2mi + 3mj and P of B is 18mi - 15mj, so using the Principle of conservation of momentum, I found v of coalesced particle to be 5i - 3j 2) kinetic energy=1/2mmodv2 and KE before impact is 98m and after is 68m, so loss is 30 joules. 4) rG=[tex]\Sigma[/tex]miri all divided by total mass...when I finally find the position vectors! 5) Velocity of the centre of mass=total linear momentum of the system...I think. 6) With position vectors for A and B, I'm not sure what to do here: add them, since the particles coalesce? 3. The attempt at a solution 3) My problem is from 3) onwards. I'm pretty sure I can figure out the rest of it once I have 3). I can't work out how to get from the velocity vectors to position vectors. I thought of integrating and using t=0 r=0 to find a particular solution, but that seems to just leave me with rA(t)=2ti + 3tj and rB(t)=6ti - 5tj, which just doesn't seem to make sense.