Average torque on a projectile of mass m (initial speed u and angle of projection θ) between initial and final positions P and Q as shown in figure, about the point of projection is:

τav→.∆t = ∆L ------(i) Here ∆t = time of flight = 2u sin θgChange in angular momentum about point of projection (initially it is zero)|∆L→| = |L→f-Li→| = (mu sin θ) Range         = (mu sin θ)(u2 sin 2θ)g = mu3sin θ sin2θgNow |τ→av| = |∆L→∆t| = mu3sin θ sin 2θg×g2u sin θ         = mu2 sin 2θ2