You and your crew must dock your 2.55 × 104 kgspaceship at Spaceport Alpha, which is orbiting Mars. In theprocess, Alpha’s control tower has requested that you ram anothervessel, a freight ship of mass 1.60 × 104 kg, latch ontoit, and use your combined momentum to bring it into dock. Thefreight ship is not moving with respect to the colossal SpaceportAlpha, which has a mass of 1.80 × 107 kg. Alpha’sautomated system that guides incoming spacecraft into dock requiresthat the incoming speed is less than 2.0 m/s.
(a) Assuming a perfectly linear alignment of yourship’s velocity vector with the freight ship (which is stationarywith respect to Alpha) and Alpha’s docking port, what must be yourship’s speed (before colliding with the freight ship) in order thatthe combination of the freight ship and your ship arrive at Alpha’sdocking port with a speed of 1.40 m/s?
(b) What will be the velocity of Spaceport Alphawhen the combination of your vessel and the freight shipsuccessfully docks with it?
(c) Suppose you made a mistake while maneuveringyour vessel in an attempt to ram the freight ship and, rather thanlatching on to it and making a perfectly inelastic collision, youstrike it and knock it in the direction of the spaceport with aperfectly elastic collision. What is the speed of freight ship inthat case (assuming your ship had the same initial velocity as youhad calculated in part (a))?
