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An artificial satellite is moving in a c...

An artificial satellite is moving in a circular or bit around the earth with a speed equal to half the magnitude of escape velocity from the earth (i) determine the height of the satellite above the earth's surface.

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Orbital velocity of a satellite at a height h above the earth's surface is
`V_(o) = (GM)/(R + h)`
Escape velocity from the earth's surface
`V_(e) = sqrt((2GM)/R)`
given `V_(o) = (V_e)/2`
`sqrt((GM)/(R+h)) = 1/4 xx(2GM)/R = (GM)/(2R)`
`h = R = 6.4 xx 10^(6)m`.
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