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≥U2Xg230 exam-style questions on Edexcel A Level Maths Projectiles, covering 6.1 Horizontal Projection, 6.2 Horizontal and Vertical Components, 6.3 Projection at Any Angle, and 6.4 Projectile Motion Formulae. Each one has a worked solution and a mark scheme showing where the marks go.