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≥u2LgPractise Edexcel A Level Maths Projection at Any Angle with exam-style questions for A Level Maths. 62 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
