The points A A\,A and B B\,B lie 120 m apart on horizontal ground. At time t=0t = 0t=0 two projectiles, P P\,P and QQQ, are launched from the points A A\,A and BBB. Projectile P P\,P is launched with speed 40 ms-1 at an angle of 30∘ 30^\circ\,30∘ to the horizontal. Projectile Q Q\,Q is launched with speed U ms−1U \text{ ms}^{-1}U ms−1 at an angle of θ \theta\,θ to the horizontal. At time t=3t = 3t=3, P P\,P and Q Q\,Q collide. Both projectiles are modelled as particles moving freely under gravity.
Find the velocity of P P\,P the instant before it collides with QQQ.
Find the size of angle θ\thetaθ.
Find the value of UUU.
State one limitation of the model that could affect the accuracy of your answers.
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.