A maintenance drone on a skyscraper drops two calibration weights into a vertical service conduit. Weight α \alpha\,α is released from rest at a height of h h\,h metres above the conduit's base. Weight β \beta\,β is released from rest tlagt_{lag}tlag seconds later from a point ρh \rho h\,ρh metres above the base, where 0<ρ<10 < \rho < 10<ρ<1. It is observed that both weights strike the base of the conduit exactly 9 seconds after weight α \alpha\,α was first released. Assuming air resistance is negligible, prove that:
tlag=9(1−ρ) t_{lag} = 9(1 - \sqrt{\rho}) tlag=9(1−ρ)Ensure every step of your derivation is clearly justified.
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.