Question

A projectile is fired vertically upwards from the surface of the earth with a velocity `Kv_(e)`, where `v_(e)` is the escape velocity and `Klt1`.If `R` is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth will be (neglect air resistance)
A. `R/(K^(2)-1)`
B. `R/(1-K^(2))`
C. `R(1-K^(2))`
D. `R/(1+K^(2))`

Answer 1

Correct Answer - B
According to the law of conservation of energy
`-(GMm)/R+1/2mK^(2)v_(e)^(2)=-(GMm)/(R+h)+0`
`v_(e)^(2)=(2GM)/R`
`-(v_(e)^(2))/2+(K^(2)v_(e)^(2))/2=-(v_(e)^(2)(R))/(2(R+h))`