A rocket is fired with a speed `v=2sqrt(gR)` near the earth's surface and directed upwards.
(a) Show that it will escape from the earth.
(b) Show that in interstellar space its speed is `v=sqrt(2gR)`.

Explanation

(a) `v=2sqrt(gR)`
`v_(e)=sqrt(2gR)`
`vgtv_(e)`
(b)
`1/2mv^(2)-(GM_(e)m)/R=1/2mv'^(2)+0 (Since U_(oo)=0)`
`1/2m.4gR-mgR=1/2mv'^(2)`
`v'=sqrt(2gR)`