Calculating the Speed of Exhaust Gas for a Rocket in Deep Space

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The discussion revolves around calculating the speed of exhaust gas from a rocket in deep space, given its acceleration and mass ejection. The conservation of momentum equation is applied, but the user struggles to isolate the speed of the exhaust gas due to the presence of the rocket's velocity in the equation. Clarification is sought on how to approach the problem, particularly regarding the use of the formula F = m*a and its relation to momentum change. Ultimately, the user finds understanding after receiving guidance on the correct application of the equations. The conversation highlights the complexities of momentum conservation in rocket propulsion scenarios.
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Homework Statement



A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.9 m/s2.

What is the speed vgas of the exhaust gas relative to the rocket?
Express your answer numerically in kilometers per second.

Homework Equations



conservation of momentum: (m1v1 + m2v2)final = (m1v1 + m2v2)initial

The Attempt at a Solution



(159/160)M(vrocket + 15.9) - (1/160)Mvgas = Mvrocket

I go on to simplify it but I can't express vgas in numerical terms, as vrocket still remains in the equation. There is no value given for this so how can I solve the question?

Pls help! Thanks! :)
 
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What's wrong with F = m*a = Δmv/Δt ?
 
hmmm... Are you saying that i should use m*a = Δmv/Δt for the change in momentum of the rocket? then wat will be the value of m? :confused:
 
ooohh! I got it now! Thanks for the help! :)
 

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