At 08:00 ship X X\,X has position vector (4i+2j)(4\mathbf{i} + 2\mathbf{j})(4i+2j) km and moves with constant velocity (−2i+3j)(-2\mathbf{i} + 3\mathbf{j})(−2i+3j) km h−1\text{h}^{-1}h−1. Another ship Y Y\,Y has position vector (−i−4j)(-\mathbf{i} - 4\mathbf{j})(−i−4j) km and moves with constant velocity (3i+5j)(3\mathbf{i} + 5\mathbf{j})(3i+5j) km h−1\text{h}^{-1}h−1.
Find the relative displacement of ship X X\,X from ship Y Y\,Y after t t\,t hours.
Find the time when X X\,X is due west of YYY.
Find the time, after 08:00, when the ships are exactly 229 \sqrt{229}\,229 km apart.
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.