Is the Velocity of a Multistage Rocket Really Lower than a Single Stage Rocket?

[musik132]

The result found in problem 7.1 says that the velocity of the two stage rocket(v1 in the derivation in the link below) < velocity of a single stage rocket(v2). Am i misinterpreting the results since I thought that the purpose of a multistage rocket was to attain higher terminal velocities. If the derivation is wrong can you show me where because the mathematical operations and the logic behind it look fine to me.

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/assignments/sol7.pdf

 

[mfb]

Well, it depends on the comparison. The typical use-case is "I want to launch x tons into orbit, how can I do that". There, a multi-stage rocket is better.
In problem 7.1, it is assumed that both rockets have the same final mass - that is completely unrealistic for the same payload. The advantage of a multi-stage rocket is the lower final mass...