A body is projected vertically upwards from the surface of the earth with a velocity equal to half of escape velocity of the earth. If `R` is radius of the earth, maximum height attained by the body from the surface of the earth is

Explanation

From law of conservation of energy,
`TE_("surface")=TE_("max Height")`
`-(GMm)/R+1/2m((V_(e))/2)^(2)=-(GMm)/(R+h)+1/2m(0)^(2)`
`-(GMm)/R+1/2m((2GM)/(4R))=-(GMm)/(R+h) " " ( :. v_(e)^(2)=(2GM)/R)`
on simplifying, wet get `h=R//3`