I will continue from your R = EL/JA expression.
J = \sigmaE
therefore,
R = EL/\sigmaEA
the E's cancel out and your answer should be R = L/\sigmaA
Hope this helps.
At the time instant where two cars meet up, the distance travelled by Car B will be 45 more than Car A...
v = x/t is the main equation for this type of question.
You need to apply conservation of momentum and energy. Initial conditions do not require you to resolve the velocity vector into components. You need to resolve the velocity vector into x and y components for the final condition.
For part a) Find out the current due to +ive ions and -ive ions. Add them to get total current...
For part b) You already know the answer >>> +ive to -ive