8. (20 points) Spheres A (mass 0.020 kg), B (mass 0.030 kg), and C (mass 0.050 kg)are approaching the origin as they slide on a frictionless air table. The initial velocities of A and B are given in the figure below. All three spheres arrive at the origin at the same time and stick together. a) What must the x- and y-components of the initial velocity of C be if all three objects end up moving at 0.50 m/s in the +x-direction after the collision?

Fig: 1

Fig: 2

Fig: 3