# Answer to Question #71480 in Classical Mechanics for Amy

Question #71480

Multistage rocket in free space (no air, no gravity). Starting at rest with an initial total mass m0, and an assumed constant exhaust speed u with respect to the ship,

(a) what is the final velocity v of the ship with respect to the ground in a two-stage process where after stage 1 mass m1 of fuel has been burnt and then mass mdrop is jettisoned to prepare for stage 2 in which a total amount of fuel m2 is burnt? [In part (a) derive a formula for v in terms of u and arbitrary masses]

(b) What is the percentage increase or decrease of the final velocity v of the ship in this

two-stage process compared to a single-stage rocket with the same exhaust speed u and initial

total mass m0, but where just m1 + m2 of fuel is burnt? [In part (b) derive a number for v’s

percentage change, and say whether it increases or decreases; like the Space Shuttle, use

mdrop = 2.5 ⨉ 105 kg, m2 = 2 mdrop , m1 = 2 m2, and m0 = 2 m1 = 2 ⨉ 106 kg]

(a) what is the final velocity v of the ship with respect to the ground in a two-stage process where after stage 1 mass m1 of fuel has been burnt and then mass mdrop is jettisoned to prepare for stage 2 in which a total amount of fuel m2 is burnt? [In part (a) derive a formula for v in terms of u and arbitrary masses]

(b) What is the percentage increase or decrease of the final velocity v of the ship in this

two-stage process compared to a single-stage rocket with the same exhaust speed u and initial

total mass m0, but where just m1 + m2 of fuel is burnt? [In part (b) derive a number for v’s

percentage change, and say whether it increases or decreases; like the Space Shuttle, use

mdrop = 2.5 ⨉ 105 kg, m2 = 2 mdrop , m1 = 2 m2, and m0 = 2 m1 = 2 ⨉ 106 kg]

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