Two objects, P P\,P and QQQ, are dropped from rest from different heights above level ground.
P P\,P is released from a height of H H\,H metres.
Q Q\,Q is released T T\,T seconds after PPP, from a height of cH cH\,cH metres, where 0<c<10 < c < 10<c<1.
Both objects are modelled as particles and hit the ground exactly 4 seconds after P P\,P was released. Air resistance is modelled as negligible.
Prove that T=4(1−c)T = 4\left(1 - \sqrt{c}\right)T=4(1−c). 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.