b) Newton's equations for the two particles are Ov av and m2 42 (1) Now introduce center of mass and relative coordinates by X=! mini + mz.12 M (2) where M = mi + ma, and solve for a, and 12 to obtain $1 = X + m2 M and $2 = X - M (3) Show that Newton's equations in these coordinates are d' X mimed'r M (4) and d' X mimz d'r av M dt2 (5) c) Now add these two equations to find d' X =0 (6) Interpret this result. d) Now divide the first equation by m, and the second by my and subtract to obtain av dt2 mz (7)