All Problems Relativistic Mechanics
Problem 1.388
A relativistic rocket emits a gas jet with non-relativistic velocity u constant relative to the rocket. Find how the velocity \(v\) of the rocket depends on its rest mass \(m\) if the initial rest mass of the rocket equals \(m_{0}\).
1.388. \(v / c=\frac{1-\left(m / m_{0}\right)^{2 u / c}}{1+\left(m / m_{0}\right)^{2 u / c}}\). Use the momentum conservation law (as in solving Problem 1.178 ) and the relativistic formula for velocity transformation.