Essential University Physics: Volume 1 (4th Edition) Clone

$h=1.7\times 10^6m$
We know that according to law of conservation of energy $\frac{1}{2}mv^2=Gm_Em(\frac{1}{r_1}-\frac{1}{r_2})$ This simplifies to: $\frac{1}{2}v^2=Gm_E(\frac{1}{r_1}-\frac{1}{r_2})$ We plug in the known values to obtain: $\frac{1}{2}(5100)^2=6.67\times 10^{-11}(5.97\times 10^{24})(\frac{1}{6.37\times 10^6}-\frac{1}{6.37\times 10^6+h})$ This simplifies to: $h=1.7\times 10^6m$