Two fire-extinguishing capsules, C1 C_1\,C1 and C2C_2C2, are launched simultaneously from a fixed point O O\,O on level ground. Both capsules move in the same vertical plane.
Capsule C1 C_1\,C1 is launched at an acute angle 2θ 2\theta\,2θ to the horizontal with speed 10v ms−1\sqrt{10}v\text{ ms}^{-1}10v ms−1. Capsule C2 C_2\,C2 is launched at an acute angle θ \theta\,θ to the horizontal with speed 4v ms−14v\text{ ms}^{-1}4v ms−1.
Both capsules land at the exact same point X X\,X on the ground. Air resistance is negligible.
By considering the horizontal range of both capsules, show that cos2θ=0.8\cos 2\theta = 0.8cos2θ=0.8.
Capsule C2 C_2\,C2 takes 2.4 seconds to travel from O O\,O to XXX. Calculate the time taken by capsule C1 C_1\,C1 to travel from O O\,O to XXX.
State one modelling assumption made regarding the projectiles.
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.