By integrating the relativistic rocket differential equation of motion from the preceding problem, show that in terms of the ratio \(\mathrm{m} / \mathrm{m}_{0}\), the relative rocket velocity \(v / \mathrm{c}\) is given by

\[\frac{v}{c}=\frac{\left.1-\left(m / m_{0}\right)\right)^{2 u / c}}{\left.1+\left(m / m_{0}\right)\right)^{2 u / c}}\]

where \(m\) is the rocket mass at any time and \(m_{0}\) is its mass at time \(t=0\) when the rocket starts from rest. We assume that the exhaust velocity \(u=\) constant.