Solving a Physics Homework Problem: Rocket Mass and Acceleration

[iamwilson]

A rocket is fired in deep space, where gravity is negligible
If the rocket has an initial mass of 6000kg and ejects gas at a relative velocity of magnitude 2000m/s , how much gas must it eject in the first second to have an initial acceleration of 25.0m/s^2 ?

im stuck on this problem, can anyone help me on it thanks!

 

[Mathemaniac]

You should post this on the https://www.physicsforums.com/forumdisplay.php?f=152".

 

[Snazzy]

You can figure out the total force using F=ma

Then you can use the impulse-momentum theorem to calculate the amount of fuel needed to be ejected in the first second.

 

[kamerling]

the mass loss of the rocket is big enough to be significant, given the fact that the
acceleration was given with 3 significant digits.
Given this, it think "how much gas must it eject in the first second to have an initial acceleration of 25.0m/s^2" is ambiguous.
I think "how much gas must it eject in the first second to have a constant acceleration of
25.0m/s^2 during this time" is the most reasonable interpretation.
You will need the rocket equation v = v_ex ln(m_0/m) that you gave in your other post for this. you know v, v_ex and m_0 (initial mass of the spaceship).

 

[iamwilson]

sorry, this is my first time using this website, so i don't know all the rules, but it's is extremely helpful