A supply crate is fired from a relief-aid pneumatic launcher positioned on a flat desert plain. The crate leaves the launcher at ground level with an initial speed of $U{m\; s}^{-1}$ directed at an angle $\theta$ above the horizontal. To reach a remote medical camp located a horizontal distance $X$ away, the crate must travel at least that distance before its first impact with the ground.

By modelling the crate as a particle and assuming constant gravitational acceleration $g$, show that the angle of projection must satisfy:

$$\sin 2\theta \ge \frac{Xg}{U^2}$$