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. `h=(R )/((2gR)/(V^(2))-1)`
B. `h=(R )/((2gR)/(V^(2))+1)`
C. `h=(R )^(2)/((2gR)/(V^(2))-1)`
D. `h=(R )^(2)/((2gR)/(V^(2))+1)`

Answer

A

Explanation

`1/2 mv^(2)=(mgR)/(1+(R )/(h)) rarr 1+(R )/(h)=2gR//v^(2)`
`therefore (R )/(h=(2gR)/(v^(2))-1`