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. They 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.
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.