A particle of mass m, charge q > 0 and initial speed v is released in?nitely far

Question

A particle of mass m, charge q > 0 and initial speed v is released in?nitely far away from a heavy nucleus of charge Q > 0. Neglect any motion of the nucleus. i) If the particle is aimed perfectly at the nucleus, what is the closest distance to the nucleus it attains? ii) If the particle is aimed imperfectly, and its closest approach to the nucleus is twice the distance of part i). What is its speed at this point of closest approach?

Explanation / Answer

using LCE K Q q / r = 0.5 m v^2====> r =2 k Q q / m v^2.... K Q q /2 *r = 0.5 m v1^2====> v1 =k Q q / m r = v/1.414 m/s

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