All Problems Laws of Conservation
Problem 1.178
A rocket ejects a steady jet whose velocity is equal to u relative to the rocket. The gas discharge rate equals \(\mu \mathrm{kg} / \mathrm{s}\). Demonstrate that the rocket motion equation in this case takes the form \[ m \mathrm{w}=\mathbf{F}-\mu \mathbf{u} \] where \(m\) is the mass of the rocket at a given moment, w is its acceleration, and \(\mathbf{F}\) is the external force.
1.178. Suppose that at a certain moment \(t\) the rocket has the mass \(m\) and the velocity \(v\) relative to the reference frame employed. Consider the inertial reference frame moving with the same velocity as the rocket has at a given moment. In this reference frame the momentum increment that the system "rocket-ejected portion of gas" acquires during the time dt is equal to dp = m dv ? dt•u = F dt. What follows is evident.