Chapter 13, Problem 54IF

The Multistage Rocket Equation. The rocket equation takes a slightly different form for a multistage rocket:

$v=n{v}_{\text{e}}\ln \left(\frac{M_{\text{i}}}{M_{\text{f}}}\right)$

where n is the number of stages.

1. a. Suppose a rocket has three stages with mass ratio M_i/M_f = 3.4 and engines that produce an exhaust velocity of 3 km/s. What is its final velocity? Is it sufficient to escape Earth?
2. b. Suppose a rocket has 100 stages with mass ratio M_i/M_f = 3.4 and engines that produce an exhaust velocity of 3 km/s. What is its final velocity? Compare it to the speed of light.