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

[ch010308]

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 v_gas 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(v_rocket + 15.9) - (1/160)Mv_gas = Mv_rocket

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

Pls help! Thanks! :)

 

[LowlyPion]

What's wrong with F = m*a = Δmv/Δt ?

 

[ch010308]

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?

 

[ch010308]

ooohh! I got it now! Thanks for the help! :)