A rocket starts vertically upward with speed `v_0`. Show that its speed v at height h is given by `v_0^2-v^2=(2gh)/(1+h/R)` where R is the radius of the earth.

An object is projected vertically upwards with a velocity u from the surface of the earth. Show that the maximum height reached by the object is h=(u^2R)/(2gR-u^2) where R is the radius of the earth. Calculate escape velocity from it.

A body is thrown vertically upwards with a velocity v from the surface of the earth. Show that the height h up to which the body will rise is given by h=(v^2R)/(2gR-v^2) here ,R=radius of the earth , g=acceleration due to gravity.

Show that the velocity of a body released at distance r from the centre of the earth, when it strikes the surface of the earth is given by , v=sqrt(2GM(1/R-1/r)) where R and M are the radius and mass of the earth. Also show that the velocity with which meteorites strike the earth's surface is equal to escape velocity.

A ball is thrown vertically upward with a speed v from a height h above the ground . The time taken for the ball to hit the ground is