Docking a Spaceship. You and your crew must dock your 2.75 × 104 kg spaceship at Spaceport Alpha, which is orbiting Mars. In the process, Alpha’s control tower has requested that you ram another vessel, a freight ship of mass 1.50 × 104 kg, latch onto it, and use your combined momentum to bring it into dock. The freight ship is not moving with respect to the colossal Spaceport Alpha, which has a mass of 1.75 × 107 kg. Alpha’s automated system that guides incoming spacecraft into dock requires that the incoming speed is less than 2.0 m/s. (a) Assuming a perfectly linear alignment of your ship’s velocity vector with the freight ship (which is stationary with respect to Alpha) and Alpha’s docking port, what must be your ship’s speed (before colliding with the freight ship) in order that the combination of the freight ship and your ship arrive at Alpha’s docking port with a speed of 1.40 m/s? (b) What will be the velocity of Spaceport Alpha when the combination of your vessel and the freight ship successfully docks with it? (c) Suppose you made a mistake while maneuvering your vessel in an attempt to ram the freight ship and, rather than latching on to it and making a perfectly inelastic collision, you strike it and knock it in the direction of the spaceport with a perfectly elastic collision. What is the speed of freight ship in that case (assuming your ship had the same initial velocity as you had calculated in part (a))?