Isaac Physics Closest Approach Question

https://isaacscience.org/questions/closest_approach_nucleus

stuck on above question, this thread ( https://isaacscience.org/questions/closest_approach_nucleus ) claims that the two particles have the same velocity at closest approach, can someone explain why that is?

thanks

Didn't you finish your A level Physics with good grade? Still doing Phyiscs?
As for your question, note that this is a collision problem.
What must be conserved regardless of whether a collision is elastic or inelastic?

haha yeah i'm studying for the PAT now,

i did consider the conservation of energy and momentum but am still left with 3 variables but only 2 equations (v_A , v_alpha and r)




^ my working so far

v_A is equal to v_alpha as posted by you.

why is that, though?

https://isaacscience.org/questions/closest_approach_nucleus
stuck on above question, this thread ( https://isaacscience.org/questions/closest_approach_nucleus ) claims that the two particles have the same velocity at closest approach, can someone explain why that is?
thanks

Hope this video will help.

Suppose t is the point in time of closest approach. If the alpha particle was moving faster than the nucleus at time t, then stepping forward in time a little bit (t + ∆t) would make them closer. If the alpha particle was moving slower than the gold nucleus, then stepping backwards in time a little bit (t - ∆t) would make them closer. In either situation, t could not be the point in time of closest approach. Thus, the only way for some point in time to be the momen of closest approach is for the two particles to be moving at constant speed at that moment.