Question

For a particle projected in a transverse direction from a height h above Earthís surface, find the minimum initial velocity so that it just grazes the surface of earth path of this particle would be an ellipse with center of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earthís surface as perigee

Answer 1

Please see attached file.......

Answer 2

For a particle projected in a transverse direction from a height h above Earthís surface, find the minimum initial velocity so that it just grazes the surface of earth path of this particle would be an ellipse with center of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earthís surface as perigee