Gravitational question (spacecraft)

[ccsmarty]

Homework Statement

An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 52.0 km. To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 27.0 m/s.
If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?

Homework Equations

mass of moon = 7.36*10^22 kg
radius of moon = 1.7374*10^6 m

The Attempt at a Solution

This is what I tried, but I got the wrong answer. Can someone please tell me what I did wrong.

Thanks in advance.

 

[Anadyne]

Can you justify why you did this?
GM/R^2 - vf^2/R = a

And later on, why is v0 = 0?

 

[ccsmarty]

Well, the first equation I got when I asked an online tutor for help.
I made v0 = 0 because I thought that the instant after the thruster fired, the velocity would be zero.

I tried doing the problem a different way today and here's my work:

However, this did not yield the right answer :(.
Any help is greatly appreciated.

 

[learningphysics]

What you did the second time around looks right to me. only thing I'm concerned with is the exact numbers, and how accurate your result needs to be...

for example you used 1.74*10^6 instead of 1.7374*10^6 (what you had in your initial post)... and 7.35*10^22 instead of 7.36*10^22 (what you had in your initial post)

those online homework things are a little problematic...

essentially your work looks right to me.