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8.69 - Spheres $A$ (mass $0.020kg$ ), $B$ (mass $0.030kg$ ), and $C$ (mass $0.050kg$ ) 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 $0.50m/s$ 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