At 6 a.m. a boat A A\,A has position vector (8i−13j)(8\mathbf{i} - 13\mathbf{j})(8i−13j) km relative to a fixed origin O O\,O and moves with constant velocity (6i−3j)(6\mathbf{i} - 3\mathbf{j})(6i−3j) km h−1\text{h}^{-1}h−1. Another boat B B\,B has position vector (38i−33j)(38\mathbf{i} - 33\mathbf{j})(38i−33j) km relative to a fixed origin O O\,O and moves with constant velocity (−9i+12j)(-9\mathbf{i} + 12\mathbf{j})(−9i+12j) km h−1\text{h}^{-1}h−1.
Find expressions for the position vectors of A A\,A and BBB, in terms of t t\,t hours after 6 a.m.
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.