- #1

lowea001

- 29

- 3

## Homework Statement

A comet in deep space picks up mass as it travels through a large stationary dust cloud. It is subject to a gravitational force of magnitude Mf acting in the direction of its motion. When it entered the cloud, the comet had mass M and speed V. After a time t, it has traveled a distance x through the cloud and its mass is M(1+bx), where b is a positive constant and its speed is v. In the case when f is a non-zero constant, show that [tex]v = \frac{ft+V}{1+bx}[/tex]

and hence find an expression for x in terms of b, V, f, and t. Then show that it is possible for the comet to move with constant speed.

## Homework Equations

Differential equations of motion for kinetics, force is rate of change of momentum (Newton's second)

## The Attempt at a Solution

So right off the bat I'm pretty sure this doesn't make sense because if the comet were to gain mass the force of gravity would change i.e. it wouldn't remain Mf. But disregarding that, my main issue is proving that the comet can move with constant speed. I know the acceleration should be shown to be an equation that has roots, but it seems pretty messy. Sorry if the solution just really is messy, but I have the feeling there's something I'm missing. Anyway, here's what I've tried: