1. The problem statement, all variables and given/known data A proton of mass m is moving with initial speed v0 directly toward the center of a nucleus of mass 31m, which is initially at rest. Because both carry positive electrical charge, they repel each other. Find the speed v' of the nucleus for the following conditions: a) the distance between the two is at it's smallest value. b) the distance between the two is very large. 2. Relevant equations p0=m*v0 KE=1/2*m*v0^2 v.cm=(v0*m)/32m 3. The attempt at a solution At first I guessed 0 for both, just because. So, since it's an elastic collision, the p and the KE remain the same before and after the collision. p=m*v0 p=m*vf+31m*v' KE=1/2*m*vo^2 KE=1/2*m*vf^2+1/2*31m*v'^2 ~~~~~~~~~~~~~~~~~~ m*v0=m*vf+31m*v' divide both sides by m v0=vf+31v' or vf=v0-31v' 1/2*m*vo^2=1/2*m*vf^2+1/2*31m*v'^2 multiply by 2/m v0^2=vf^2+31v'^2 exchange vf v0^2=v0^2-62v0*v'+962v'^2+31v'^2 some algebra 62v0*v'=993v'^2 v'=62/993v0 or 0.0624*v0 checking this, this is the case during (b) but not during (a) I feel like I've missed something, probably not considering the fact that the two are pushing against each other at close distances but I'm not 100% sure how to account for that.