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.
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.