Forming a differential equation for a body whose mass changes

[nokia8650]

http://img8.imageshack.us/img8/2166/58510589xd3.th.jpg

I was having trouble following various aspects of the above explanation:

Why does the ejected mass have a speed "v-u" at the start of the interval?

Why is the oif the body mass (m + (Delta)m) and not (m - (Delta)m).

Thanks

 

[djeitnstine]

The speed has to be v-u since the mass is being ejected relative to the body it is being ejected from. To an outside observer it would be v+u since the mas and the body are apparently going in the same direction.

"Why is the oif the body mass (m + (Delta)m) and not (m - (Delta)m)."

As the body moves the mass changes $$\delta m$$ doesn't necessarily means mass is added...simply means a change in mass at another time t