Can somebody show me step by step how to solve this physics question?

Physics
Tutor: None Selected Time limit: 1 Day

A rocket is fired in a gravity-free environment in deep space. The rocket has an initial mass of 8000 kg and ejects gas with a velocity of 2000 m/s. How much gas must be ejected in the first second to give the rocket an acceleration of 30.0 m/s?

Jun 7th, 2015

Thank you for the opportunity to help you with your question!

thrust of a rocket = -uR = Th

u = velocity of exhaust relative to rocket

R = rate of mass ejection

we need R

Newton's II law: F̂ᵣₑ = mâ

Th - mg = ma (gravity free, hence g = 0)

=> Th = ma = 240000 N = uR = 2000R

=> R = 240000/2000 = 120 kg/s

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 7th, 2015

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