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−1U \text{ m s}^{-1}U m s−1 directed at an angle θ \theta\,θ above the horizontal. To reach a remote medical camp located a horizontal distance X X\,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 ggg, show that the angle of projection must satisfy:
sin2θ≥XgU2 \sin 2\theta \ge \frac{Xg}{U^2} sin2θ≥U2Xg