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A single-stage rocket needing to overcome both air resistance and gravity during launch faces an even harder mass ratio than the idealized escape-velocity case. What mass ratio does this real case require?
AA ratio of about m0 divided by 180
BThe exact same ratio of m0 divided by 88
CA ratio of about m0 divided by 44
DA ratio of about m0 divided by 8
Answer & Solution
Correct answer: A. A ratio of about m0 divided by 180
1. The idealized calculation, ignoring air resistance and gravity's effect during the burn, gave a remaining mass of about m0 divided by 88.
2. Including air resistance and gravitational force makes the achievable mass ratio even less favorable.
3. With those effects included, the remaining mass can only be about m0 divided by 180.
4. This is a harder requirement than the idealized 88 ratio, which is exactly why multistage rockets become the practical solution.
_Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.7 Introduction to Rocket Propulsion_
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