Rocket Problem

1. Feb 29, 2004

NanoTech

A rocket is moving away from the solar system at a speed of 6.0 x 10^3 m/s. It fires its engine, which ejects exhaust with a speed of 3.0 x 10^3 m/s relative to the rocket. The mass of the rocket at this time is 4.0 x 10^4 kg, and its acceleration is 2.0 m/s/s.

A) What is the thrust of the engine?

I thought to use the equation T = ma ? T = (4.0 x 10^4 kg)(2.0m/s/s) = 8.0 x 10^4 N.

B) At what rate, in kilograms per second, is exhaust ejected?

I'm stumped on this one, I thought that's what Thrust was?

I thought to maybe use the equation: Vf-Vi = Vrel ln(Mi/Mf) but i don't even know how to use it in this situation... Any help would be great, thanks! ~Dave

2. Feb 29, 2004

Moose352

I think you need to use momentum.

3. Feb 29, 2004

Staff: Mentor

Right. (Assuming that the gravitational force is negligible and that the thrust is the only force on the rocket.)
How could an exhaust rate be equal to a force? The units don't match.

Anyhow, thrust is given by Vrel*dM/dt.

4. Mar 1, 2004

NanoTech

ok, so for part B. i take the derivative of the mass, then multiply it by the Vrel. thanks. ~Dave

5. Mar 1, 2004

Staff: Mentor

For part B you are to find the exhaust rate, which is dM/dt. Set the thrust equal to what you found in part A, then solve for dM/dt.