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?
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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
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