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.
Practise Edexcel A Level Maths Projectiles with exam-style questions for A Level Maths. 73 questions covering Horizontal Projection, Horizontal and Vertical Components, Projection at Any Angle, and Projectile Motion Formulae, 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.