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Classical Mechanics Level 4

A rocket, dry mass 500 kg 500\text{ kg} can eject fuel at 1000 ms − 1 1000\text{ ms}^{-1} . Taking g = 10 ms − 2 g=10\text{ ms}^{-2} what mass of fuel is required for the rocket to hover for 60 seconds?

Give your answer to 1 decimal place.

Inspiration .


The answer is 411.1.

William Whitehouse by William Whitehouse , 22, United Kingdom

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1 solution

I=1000 Δ \Delta M -> F=-1000 δ M δ t \frac{\delta M}{\delta t} =10M (as force from fuel ejection =gravitational forces)

Solving this differential equation gives M = A e − t 100 M=Ae^{-\frac{t}{100}} and it is known that at t=60s M=500kg. Plugging these numbers gives A = 500 e 3 / 5 ≈ 911.1 A=500e^{3/5} \approx 911.1 . This includes the rockets mass so 911.1-500=411.1.

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