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 from A A\,A towards B B\,B with speed 40 ms-1 at an angle of 30∘ 30^\circ\,30∘ to the horizontal. Projectile Q Q\,Q is launched from B B\,B towards A A\,A 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.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.