A projectile is projected with a speed K Ve where Ve is escape velocity and K is a constant less than one. The maximum height reached by it from the centre of earth will be :

Options

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

Answer

C

Explanation

According to conservation of energy
`(GMm)/R =(GMm)/(R+h)=1/2mK^(2)v_(e)^(2)`
or `gR- (gR^(2))/(R+h)=1/2K^(2)(sqrt(2gR))^(2)`
or `R/(R+h)=1-K^(2)`or `R+h=R/(1-K^(2))`