A supply crate is fired from a pneumatic launcher standing on a flat horizontal plain. The crate leaves the launcher at ground level with initial speed U U\,U m s−1^{-1}−1 at an angle θ \theta\,θ above the horizontal.
To reach a medical camp a horizontal distance X X\,X metres away, the crate must travel at least that distance before its first impact with the ground.
The crate is modelled as a particle moving freely under gravity, with air resistance negligible and gravitational acceleration g g\,g constant.
By finding the time of flight and hence the horizontal distance travelled, show that sin2θ≥XgU2\sin 2\theta \ge \dfrac{Xg}{U^2}sin2θ≥U2Xg.
91 exam-style questions on OCR (MEI) A Level Maths 3.3 Projectiles (A-level only), covering 3.3.1 Model motion under gravity using vectors (A-level only), 3.3.2 Position, velocity, range and maximum height (A-level only), 3.3.3 Find the initial velocity of a projectile (A-level only), 3.3.4 Equation of the trajectory (A-level only), and 3.3.5 Solve simple projectile problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.