With what velocity should a particle be projected so that its height becomes equal to radius of earth ?

With what velocity should a particle be projected so that its maximum height attained becomes equal to radius of earth ?

With what minimum velocity v should a particle be thrown horizontally from a height h above the surface of the earth of mass M so that it does not fall back on the earth ? Radius of earth is R ?

At what angle to the horizontal should an object be projected so that the maximum height reached is equal to the horizontal range.

By what facter should the velocity of a moving particle be changed so that its kinetic energy becomes 1/16 of its intial value ?

A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is