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 (ii) If the satellite is stopped suddenly in its orbit or allowed to fall freely on the earth, find the speed with which it hits the surface of the earth take `g = 9.8 ms^(-2)`, radius of the earth = 6400 km.

Explanation

Let V be the speed, with which the satellite hits the earth when suddenly stopped if m be the mass of the satellite, then by the conversion of energy initial P.E. At height h = R
Final P.E on the surface of earth + K.E of the satellite
or `-(GMm)/(2h) = -(GMm)/R + 1/2 mV^2`
`V = sqrt((GM)/(R)) = sqrt((gR^2)/(R)) = sqrt(gR)`
`= sqrt(9.8 xx 6.4 xx 10^(6))`
`= 7.92 xx 10^(3) ms^(-1)`
`= 7.92 km s^(-1)`.