Classical Mechanics - Taylor. Prob 3.2, 3.6, 3.7, 3.9: Conservation of Momentum/Rockets

Classical Mechanics - John R. Taylor
Chapter 3: Momentum and Angular Momentum
3.1: Conservation of Momentum
3.2: Rockets

Prob 3.2: A shell traveling with speed v0 exactly horizontally and due north explodes into two equal-mass fragments. It is observed that just after the explosion one fragment is traveling vertically up with speed v0. What is the velocity of the other fragment?

Prob 3.6: In the early stages of Saturn V rocket's launch, mass was ejected at about 15000 kg/s, with a speed v_ex = 2500 m/s relative to the rocket. What was the thrust on the rocket? Convert this to tons (1 ton = 9000 newtons) and compare with the rocket's initial weight (about 3000 tons).

Prob 3.7: The first couple of minutes of the launch of a space shuttle can be described very roughly as follows: The initial mass is 2 x 10^6 kg, the final mass (after 2 minutes) is about 1 x 10^6 kg, the average exhaust speed v_ex is about 3000 m/s, and the initial velocity is, of course, zero. If all this were taking place in outer space, with negligible gravity, what would be the shuttle's speed at the end of this stage? What is the thrust during the same period and how does it compare with the initial total weight of the shuttle (on earth)?

Prob 3.9: From the data in Problem 3.7, you can find the space shuttle's initial mass and the rate of ejecting mass -dm/dt (which you may assume is constant). What is the minimum exhaust speed v_ex for which the shuttle would just begin to lift as soon as burn is fully underway? (hint: The thrust must at least balance the shuttle's weight.)