Answer:
[tex]23.89x10^{6}[/tex] ft
Step-by-step explanation:
[tex]\frac{V^{2} }{R^{2} } = \frac{2g}{R+h} \\[/tex] This is the formula to find satellite's escape velocity V , where R is earth's radius, h is the satellite's height from the earth surface and g is the earth's gravitational constant.
[tex]R^{2}(R+h) \frac{V^{2} }{R^{2} } =R^{2} (R+h)\frac{2g}{R+h}[/tex] (Multiplying to clear the fractions)
(R+h)[tex]V^{2} =R^{2} 2g[/tex]
[tex]R+h=\frac{2R^{2}g }{V^{2} }[/tex]
[tex]h= \frac{2R^{2} g}{V^{2} } -R[/tex]
Now, we can determine height of satellite from the surface of the earth
by putting the values in above equation
[tex]h= \frac{2 * (3960)^{2}*32.2 }{6.5^{2} } -3960\\h= 23.902 x10^{6} - 3960\\ h=23.89x10^{6} ft[/tex]
