Charge particle is moving under the influence of a point nucleus. Show that the orbit of the particle is an ellipse
Answers
Initial position X of Centre of Mass (CM) is given by, X =begin mathsize 12px style fraction numerator m subscript 1 X subscript 1 space end subscript plus space m subscript 2 X subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction space equals space fraction numerator 1 cross times 2 space plus space 1 cross times 8 over denominator 1 plus 1 end fraction space equals space 5 space m end style
velocity V of CM is given by, V =begin mathsize 12px style fraction numerator m subscript 1 cross times v subscript 1 space plus space m subscript 2 cross times v subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction space equals space fraction numerator 1 cross times 5 space minus space 1 cross times 3 over denominator 1 plus 1 end fraction space equals space 1 space m divided by s end style
hence position of CM after 1 second = 5+1×1 = 6 m