A Multistage Rocket.? Suppose the first stage of a two stage rocket has total mass 12,000 kg, of which 9000 kg is fuel. The total mass of the second stage is 1000 kg, of which 700 kg is fuel. Assume that the relative speed ?v?ex of ejected material is constant, and ignore any effect of gravity. (The effect of gravity is small during the firing period if the rate of fuel consumption is large.) (a) Suppose the entire fuel supply carried by the two-stage rocket is utilized in a single-stage rocket with the same total mass of 13,000 kg. In terms of ?v?ex, what is the speed of the rocket, starting from rest, when its fuel is exhausted? (b) For the two-stage rocket, what is the speed when the fuel of the first stage is exhausted if the first stage carries the second stage with it to this point? This speed then becomes the initial speed of the second stage. At this point, the second stage separates from the first stage. (c) What is the final speed of the second stage? (d) What value of ?v?ex is required to give the second stage of the rocket a speed of 7.00 km/s?

Solution 113P Introduction In this problem we will use the equation of rocket motion to calculate the velocities. Step 1 We know that the change in the velocity of a rocket is given by Here And Hence, the change in velocity is Now since the rocket started from the rest, the velocity of the rocket when all the fuel is exhausted is