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.
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.