Rocket Velocity and Acceleration Calculation

[wr8899]

Homework Statement

Consider a rocket in space that ejects burned fuel at a speed of v_ex= 2.0 km/s with respect to the rocket. The rocket burns 10 % of its mass in 340 s (assume the burn rate is constant).

(a) What is the speed v of the rocket after a burn time of 170.0 s? (suppose that the rocket starts at rest; and enter your answer in m/s) ?
(b) What is the instantaneous acceleration of the rocket at time 170.0 s after the start of the engines?(in m/s^2 ) ?

Homework Equations

v_f = -v_ex*ln(m_final/m_initial) - g*burn time

The Attempt at a Solution

I plugged in the data, getting -2000*ln(0.95) - g*170, but got the velocity wrong. I have no idea where I went wrong, and I am stuck here, along with finding the acceleration. Can someone please help me get unstuck here. Thanks and sorry to be a bother.

 

[BOYLANATOR]

EDIT : What I wrote here was wrong

 

[BOYLANATOR]

What is g in space?

 

[mfb]

In addition to BOYLANATOR's post, where does the 0.95 come from?

 

[wr8899]

0.95 comes from the final mass over initial mass, since after 170.0 seconds, you have 95% of the original mass left (other 5% mass was burned already)

 

[mfb]

Oh 10% in 340s... okay, I missed that part. Where is the point in the second 170 seconds?

 

[wr8899]

what you mean?

 

[wr8899]

Because, 10% of mass burned every 340 seconds, so 5% of mass burned every 170 seconds, therefore I got the 0.95

 

[mfb]

I agree, I didn't read the problem statement careful enough.
I was just wondering why the problem statement gives the fuel burnt in 340 seconds and then just asks for the rocket after 170 seconds.

 

[BOYLANATOR]

Did you manage to solve the problem?