For the two questions that follow, please write out your detailed solution on paper. Please include a sketch of forces, equation(s) you used, algebraic manipulations, substituted values, and the final answer with units.

A 23 g ball of clay moving west at 12 m/s collides with and sticks to a 31 g ball of clay moving south at 21 m/s.

a) What is the final velocity of the resulting 54 g mass of clay? Please give the final velocity to 3 significant figures with the units. Draw labeled diagrams to show the velocities and masses before and after the collision along with your coordinate system with labeled axes. (10 points, out of which 4 points are for the figure with a coordinate system, showing before and after situations for the labeled masses, 4 points are for calculations of final velocities in the x- and y-directions and 1 point is for the answer to 3 significant figures with units)

b) What is the direction in which the combined mass moves after the collision? (5 points, out of which 2 points are a figure showing the angle with respect to the vectors v_fx and v_fy, and 1 point for the description of the angle, e.g., "north of east").