A specialized rescue apparatus at sea fires a tethered buoy from a deck towards a distress signal. The signal is located on a floating platform at a horizontal distance of LLL metres from the launch site. The buoy is projected with an initial velocity of u m s−1u \text{ m s}^{-1}u m s−1 at an elevation angle of β\betaβ to the horizontal. By modelling the buoy as a particle and the platform as being at the same horizontal level as the launch point, and neglecting air resistance, prove that for the buoy to reach at least the distance of the platform, the angle β\betaβ must satisfy the condition:
sin2β≥Lgu2 \sin 2\beta \ge \frac{Lg}{u^2} sin2β≥u2Lg91 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.