# A spacecraft encounters a stationary dust cloud of density rho.

1. Jun 24, 2012

### 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.

Last edited: Jun 24, 2012
2. Jun 24, 2012

### 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 $\dot{m}v+m\dot{v} = 0$.

3. Jun 24, 2012

### AbigailM

Thanks for the help Filip.