The unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively. At midday a boat A A\,A is 7 km east of a fixed origin O O\,O and is moving with constant velocity (−4i+3j)(-4\mathbf{i} + 3\mathbf{j})(−4i+3j) km h−1\text{h}^{-1}h−1. At the same time, another boat B B\,B is 12 km north of O O\,O and is moving with uniform velocity (−3i+2j)(-3\mathbf{i} + 2\mathbf{j})(−3i+2j) km h−1\text{h}^{-1}h−1.
Show that, at time t t\,t hours after midday, the position vector of A A\,A is [(7−4t)i+3tj][(7 - 4t)\mathbf{i} + 3t\mathbf{j}][(7−4t)i+3tj] km and find a similar expression for the position vector of B B\,B at this time.
363 exam-style questions on Edexcel A Level Maths Further Kinematics, covering 8.1 Vectors in Kinematics, 8.2 Vector Methods with Projectiles, 8.3 Variable Acceleration in One Dimension, 8.4 Differentiating Vectors, and 8.5 Integrating Vectors. Each one has a worked solution and a mark scheme showing where the marks go.