A spaceship is launched into a circular orbit close to the earth's surface . What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull. Radius of earth `= 6400 km`, `g = 9.8m//s^(2)`.

Explanation

For satallite closed to earth
`v_(0)=sqrt((GM_(e))/(R_(e)))=sqrt(gR_(e))=8km//s`
Escape velocity from the surface of earth
`v_(e)=sqrt((2GM_(e))/(R_(e)))=sqrt(2gR_(e))=11.2 km//s`
(i) Additional velocity `=v_(e)-v_(0)=11.2-8=3.2 km//s`
(ii) Percentage increases in velocity `=((v_(e))/(v_(0))-1)xx100`
(iii) Percentage increases in `K.E.`
`((1/2mv_(e)^(2))/(1/2mv_(0)^(2))-1)xx100`
`=(2-1)xx100=100%`