A projectile of mass \(m\) is launched from the ground with the initial speed \(v_0\) at an angle \(30^{\circ}\) from the horizontal. Take the ground to be horizontal. Ignoring the drag, the magnitude of Hamilton's action \(\int L\,dt\) for the particle from the beginning till it hits the ground is \(f \times \left(\dfrac{mv_0^{3}}{g}\right)\). The value of \(f\) (rounded off to two decimal places) is .