A rocket is fired in a gravity-free environment in deep space. The rocket has an

Question

A rocket is fired in a gravity-free environment in deep space. The rocket has an inital mass of 8000 kb 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?

Explanation / Answer

As there are no external forces on the rocket momentum can be conserved at any instant mg*vg=mr*vr --->eq 1 mg,mr are masses of gas and rocket at some time vg,vr are velocities of ejecting gas and rocket Differentiate eq 1 on both sides mg'*vg=-mg'*vr + mr*vr' [mr=total mass-mg] =-mg'*(0)+ 8000*30 [ initial velocity of rocket vr=0,initial mass of rocket =800 kg,acceleration=30] mg'=240000/2000=120 kg/s S0 120 kg mass must be ejected in the first second to give the rocket an acceleration of 30.0 m/s

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