Question

A body is projected vertically from the surface of the earth of radius rr with a velocity equal to half of the escape velocity. the maximum height reached by the body is:

Answer 1

v= √ 2gh 

Velocity (escape ) = √ 2 G M / R 

v = 1/2 Velocity ( escape )    -------- ( Given )

that's why 

  1/2 × √ 2 G M / R  = √ 2gh 

GM/ 4 R = g h 

h= GM / 4Rg 

h = max . Height reached by body