The total time of the journey in the presence of air resistance (more specifically, when F a i r = − − k v ) can be calculated by the same strategy as above, namely, we solve the equation y ( t ) = 0 . While in the case of zero air resistance this equation can be solved elementarily, here we shall need the Lambert W function. The equation y ( t ) = − − g μ μ t + 1 μ μ ( v y 0 + g μ μ ) ( 1 − − e − − μ μ t ) = 0 is of the form c 1 t + c 2 + c 3 e c 4 t = 0 , and such an equation can be transformed into an equation solvable by the W function (see an example of such a transformation here). Some algebra shows that the total time of flight, in closed form, is given as