A stone is thrown from a point O O\,O on horizontal ground with velocity k(5i+j)ms−1k(5\mathbf{i} + \mathbf{j})\text{ms}^{-1}k(5i+j)ms−1, where k k\,k is a constant. The maximum height of the stone above the ground is 5 m.
Find the exact value of kkk.
Find the horizontal distance from O O\,O to the point where the stone returns to the ground.
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.