Question

What is the minimum initial velocity a rocket must be fired if it is to be able to reach the target 1000 km away?

Answer 1

$$0.5mv^2=\frac{GmM}{R}-\frac{GmM}{R+h}\\0.5v^2=\frac{GM}{R}-\frac{GM}{R+h}\\0.5v^2=\frac{(5.97\cdot10^{24})(6.67\cdot10^{-11})}{6.37\cdot10^{6}}-\frac{(5.97\cdot10^{24})(6.67\cdot10^{-11})}{6.37\cdot10^{6}+10^{6}}\\v=4120\frac{m}{s}$$