Two-dimensional particle trajectories, a sphere of radius R is fired horizontally (in the x direction) at high velocity in still air above level ground. As it leaves the propelling device, an identical sphere is dropped from the same height above the ground (in the y direction). 

(a) Develop differential equations from which the particle trajectories can be computed, and that will permit comparison of the behavior of the two spheres. Include the effects of fluid friction, and make the assumption that steady-state friction factors may be used (this is a "quasi-steady-state assumption"). 

(b) Which sphere will reach the ground first? 

(c) Would the answer to (b) have been the same if the sphere Reynolds numbers had been in the Stokes' law region?