Two spheres having masses $M$ and $2 M$ and radii $R$ and $3 R,$ respectively, are simultaneously released from rest when the distance between their centers is $12 R$ Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. (a) What $t w o$ isolated system models are appropriate for this system? (b) Write an equation from one of the models and solve it for $\overrightarrow{\mathbf{v}}_{1},$ the velocity of the sphere of mass $M$ at any time after release in terms of $\overrightarrow{\mathbf{v}}_{2},$ the velocity of $2 M .$ (c) Write an equation from the other model and solve it for speed $v_{1}$ in terms of speed $v_{2}$ when the spheres collide. (d) Combine the two equations to find the two speeds $v_{1}$ and $v_{2}$ when the spheres collide.