A spacecraft encounters a stationary dust cloud of density rho.

[AbigailM]

I'm currently preparing for a prelim and just wondering if my solution to this problem is correct. I did a plot of v(t) and it looked reasonable. You can find the question and solution both at http://oi50.tinypic.com/2e3v4e8.jpg.

The Problem states:

A spacecraft of mass m_0 and cross-sectional area A is coasting with a velocity v_o when it encounters a stationary dust cloud of density rho. Assuming that all the dust sticks to the spacecraft and that A remains unchanged, find the subsequent motion, i.e. v(t) of the spacecraft .

Update: I seem to have made an error by pulling v outside of the integral.

Thank you all for the help.

 

[Filip Larsen]

Welcome to PF!

You may find it easier to establish the acceleration of the rocket with its accumulating mass directly from the differential of the conservation of momentum, i.e. from $\dot{m}v+m\dot{v} = 0$.

 

[AbigailM]

Thanks for the help Filip.