A spacecraft is launched in a circular orbit very close to earth. What additional velocity should be given to the spacecraft so that it might escape the earth's gravitational pull.

Options

A. `11.2km//s`
B. `3.3km//s`
C. `8km//s`
D. `20.2km//hour`

Answer

B

Explanation

For the spaceship, the orbital velocity `v_(0)=sqrt((GM)/(R ))`
When it is orbitting very close to the surface of the earth and it is projected from the surface of the earth, the escape velocity, `v_(e)=sqrt((2GM)/(R ))`
`therefore (v_(e))/(v_(0))=sqrt(2)` or `v_(0)=(v_(e))/(sqrt(2))=(11.2)/(1.414)=7.9`
`therefore` Additional velocity `=v_(e)-v_(0)=11.2-7.9=3.3 km//s`