A rocket is launched vertical from the surface of the earth of radius R with an initial speed `v`. If atmospheric resistance is neglected, then maximum height attained by the rocket is

Options

A. `(R)/(((2gR)/(2v^(2))-1))`
B. `R((gR)/(2v^(2))-1)`
C. `(R)/(((2gR)/(v^(2))-1))`
D. `R((2gR)/(v^(2))-1)`

Answer

c

Explanation

`(g)/(R)=(u^(2))/(v_(e)^(2)-r^(2))=(v^(2))/(v_(e)^(2)-v^(2))`
`h=(R)/([(v_(e)^(2))/(v^(2))-(v^(2))/(v^(2))])=(R)/([(v_(e)^(2))/(v^(2))-1])=(R)/([(2GM)/(v^(2)R)-1])`
`=(R)/([(2gR^(2))/(v^(2)R)-1])=(R)/([(2gR)/(v_(R)^(2))-1])`