'Rocket equation'(Physics by example, Rees, pr. 16)

[bentley4]

Questions:
1. How can one tell that at time t+dt the velocity of the rocket is an infinitesimal quantity and the velocity of the ejected product a real quantity?
2. Why is for the mass of the rocket not simply written m-dm and why for the mass of the ejected product not written (+)dm?

 

[Spinnor]

The rocket starts from rest at time = t. If dt is small enough then the rocket has gained little velocity at time t + dt.

I'm not sure what you mean when you say,

"...the velocity of the ejected product a real quantity?"

You write,

"Why is for the mass of the rocket not simply written m-dm and why for the mass of the ejected product not written (+)dm?"

That would have made more sense to me as well, but it still works out.

 

[bentley4]

Hi Spinnor,

I'm not sure what you mean when you say,

"...the velocity of the ejected product a real quantity?"

In the solution, the velocity of the product is denoted with v_r. So they are saying that the velocity is a real quantity (consists of a real number) as opposed to an infinitesimal quantity (like dv, a hyperreal number).

The rocket starts from rest at time = t. If dt is small enough then the rocket has gained little velocity at time t + dt.

Ok, I think I understand this now.