(Solved): 8.69 - Spheres A (mass 0.020kg ), B (mass 0.030kg ), and C (mass 0.050kg ) are approachin ...

8.69 - Spheres $$A$$ (mass $$0.020\mathrm{kg}$$ ), $$B$$ (mass $$0.030\mathrm{kg}$$ ), and $$C$$ (mass $$0.050\mathrm{kg}$$ ) are approaching the origin as they slide on a frictionless air table. The initial velocities of $$A$$ and $$B$$ are given in Fig. P8.69. 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 are to end up moving at $$0.50\mathrm{m}/\mathrm{s}$$ in the $$+x$$-direction after the collision? (b) If $$C$$ has the velocity found in part (a), what is the change in the kinetic energy of the system of three spheres as a result of the collision? Figure P8.69