Two research probes are dropped from rest at different altitudes during a planetary landing simulation. Probe P1 P_1\,P1 is released from an altitude of A A\,A metres. Probe P2 P_2\,P2 is released δ \delta\,δ seconds after P1 P_1\,P1 from an altitude of rArArA, where r r\,r is a constant such that 0<r<10 < r < 10<r<1. Both probes reach the surface at the same time, exactly 6 seconds after the release of P1P_1P1. Assuming the probes move under constant acceleration due to gravity g g\,g and air resistance is ignored,
prove that
δ=6(1−r)\delta = 6(1 - \sqrt{r})δ=6(1−r)
Fully justify your answer.
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.