A cricket ball is hit from the ground with an initial velocity of k(2i+5j)ms−1k(2\mathbf{i} + 5\mathbf{j})\text{ms}^{-1}k(2i+5j)ms−1, where k k\,k is a constant. The maximum height above the ground reached by the ball is 50 m.
Find the exact value of kkk.
Find the horizontal distance from the point of projection to the point where the ball strikes the ground.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.