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.
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.