Sphere A (mass m), moving with speed 3v, collides with sphere B (mass 2m) which is moving in the opposite direction with speed v. The two spheres then combine, calculate the resulting velocity of the combined spheres.

Sphere A has mass m and velocity +3v so its initial momentum is 3mv. Sphere B has mass 2m and velocity -v so its initial momentum is -2mv. Therefore we can say:3mv - 2mv = M_cv_c, where M_c and v_c are the mass and velocity of the combined spheres respectively. The mass will simply be the sum of the masses of A and B, thus M_c = 3m. We can therefore calculate v_c by:3mv - 2mv = 3mv_c -> mv = 3mv_c -> v = 3v_c Therefore the final velocity of the spheres is v/3.