Answer
$h=2.64\times 10^6m$
Work Step by Step
We know that
$(R_E+h)^2=2R_E^2$
This simplifies to:
$h=\sqrt{2-1}R_E$
We plug in the known values to obtain:
$h=(\sqrt {2}-1)(6.37\times 10^6)$
$h=2.64\times 10^6m$
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