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A Saturn V rocket has a liftoff mass of 2.80 times ten to the sixth kg, a fuel burn rate of 1.40 times ten to the fourth kg per second, and an exhaust velocity of 2.40 times ten to the third m/s. Using g = 9.80 m/s squared, what is its initial acceleration?
AAbout 12.0 m/s squared
BAbout 2.20 m/s squared
CAbout 9.80 m/s squared
DAbout 0.20 m/s squared
Answer & Solution
Correct answer: B. About 2.20 m/s squared
1. The rocket acceleration equation is a equal to (v_e divided by m) times (delta m over delta t), minus g.
2. Substituting the given values, a equals (2.40 times ten to the third m/s divided by 2.80 times ten to the sixth kg) times 1.40 times ten to the fourth kg/s, minus 9.80 m/s squared.
3. The first term works out to about 12.0 m/s squared.
4. Subtracting the acceleration due to gravity gives about 12.0 minus 9.80, which is 2.20 m/s squared.
5. 12.0 m/s squared is the thrust term alone before subtracting gravity, and 9.80 m/s squared is just g itself with no thrust included.
_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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