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.
Practise Edexcel A Level Maths Projectiles with exam-style questions for A Level Maths. 73 questions covering Horizontal Projection, Horizontal and Vertical Components, Projection at Any Angle, and Projectile Motion Formulae, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.