Two astronauts (let's say George and Sandra) are drifting somewhat towards one another while in deep space. Specifically, George is moving with speed V_g and Sandra is moving with speed V_s= 8V_g/2. When George and Sandra collide with one another, they hang on tight and move off in the same direction with speed V_f = V_g/2. George has mass M_g= 1.60 m_s where M_s is Sandra's mass.

(a) What are the magnitude P_g of George's momentum, P_s the magnitude of Sandra's momentum, and !! the magnitude of their combined final momentum. Express your answers in terms of M_s and V_g .

(b) Chose a coordinate system for this problem, and draw arrows representing the vectors p_g^→, p_s^→, p_f^→. Be sure to include angles to represent the momentum directions. Define any and all symbols that you introduce. ((Hint: A clever choice of coordinate system here will simplify the rest of this problem a great deal.))

(c) Using the diagram that you drew for part (b), determine the angle θ₀ at which the two astronauts collided.

(d) Clearly this collision is completely inelastic because the two astronauts "stick together", but just how inelastic is the collision? In other words, by what percent has their kinetic energy decreased.