The points X X\,X and Y Y\,Y lie 100 m apart on horizontal ground. At time t=0t = 0t=0 two balls, M M\,M and NNN, are projected from X X\,X and Y Y\,Y respectively. Ball M M\,M is projected with speed 30 ms-1 at an angle of 45∘ 45^\circ\,45∘ to the horizontal. Ball N N\,N is projected with speed U ms−1U \text{ ms}^{-1}U ms−1 at an angle of ϕ \phi\,ϕ to the horizontal. At time t=2.5t = 2.5t=2.5, the balls collide in mid-air. Both balls are assumed to be particles in free flight.
Find the velocity of M M\,M the instant before it collides with NNN.
Find the size of angle ϕ\phiϕ.
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.