A particle is projected upward from the surface of earth(radius R) with a K E equal to half the - Physics - Gravitation

Question

A particle is projected upward from the surface of earth(radius R)
with a K E equal to half the minimum value needed for it to escape
from earth's gravity To what height does it rises above the surface
of earth?

Vara · Accepted Answer

KE needed to escape from the surface:
E=12mve2   =12m2Gmr2   =12m2Gmr   =GMmr

PE at the surface of Earth + 12E= PE at the maximum height
-GMmr+12GMmr=-GMmr+h-12GMmr=-GMmr+h              12r=1r+h               2r=r+h                h=r

Answer: h = r

A particle is projected upward from the surface of earth(radius R) with a K.E. equal to half the minimum value needed for it to escape from earth's gravity. To what height does it rises above the surface of earth?