(Drag in 3D) We have seen in lecture that the governing equations for a projectile with quadratic air resistance are given, in vector form, by/dt= g-c/m UV.

(1)In this problem, we will still take the y-direction to point opposite gravity, so that g=-gj,but we will consider motion in three dimensions, such that v=v₂i+vyj+v₂k.

(a) Derive the three equations of motion governing Ux, Uy,and V₂.

(b)Suppose that v₂(0) = 0. Based on the equations you derived in part (a),argue that u will always be zero.

(c) Based on your response to part (b), argue that, in the absence of wind,projectile motion is confined to the plane defined by the initial velocity components.