In a decorative water feature, two laminar jets of water are projected from a nozzle at the origin O O\,O on the water's surface. Jet A A\,A is projected at an acute angle α \alpha\,α to the horizontal with speed u m s−1u \text{ m s}^{-1}u m s−1. Jet B B\,B is projected at an acute angle 2α 2\alpha\,2α to the horizontal with speed 2u m s−12u \text{ m s}^{-1}2u m s−1. Both jets travel in the same vertical plane and enter the pool at the exact same point W W\,W on the surface. Air resistance is neglected.
Show that cos2α=18\displaystyle \cos 2\alpha = \frac{1}{8}cos2α=81.
Jet B B\,B takes 1.2 seconds to travel from O O\,O to WWW. Calculate the time taken by Jet A A\,A to travel from O O\,O to WWW.
State one modelling assumption made regarding the jets of water.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.