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 gravitational acceleration g g\,g constant and air resistance negligible.
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.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.