Drag Force and Terminal Velocity Explained
Explain qualitatively how drag force (fluid resistance) affects a falling object, leading it to reach a constant terminal velocity.
Part a
Derive the differential equations for the horizontal and vertical components of projectile motion when a drag force proportional to \(v^2\) is present. Assume the drag force is given by \(F_d = -k v^2\) where \(v = \sqrt{v_x^2+v_y^2}\), and show how this force is decomposed into its components.