Randall D. Knight — Impulse and Momentum: Problem 75

a. To understand why rockets often have multiple stages, first consider a single-stage rocket with an empty mass of 200 kg, 800 kg of fuel, and a 2000 m/s exhaust speed. If fired in deep space, what is the rocket’s maximum speed? b. Now divide the rocket into two stages, each with an empty mass of 100 kg, 400 kg of fuel, and a 2000 m/s exhaust speed. The first stage is released after it runs out of fuel. What is the top speed of the second stage? You’ll need to consider how the equation for \(v_{\text{max}}\) should be altered when a rocket is not starting from rest.