At 6 a.m. a boat A A\,A has position vector (7i−9j)(7\mathbf{i} - 9\mathbf{j})(7i−9j) km relative to a fixed origin O O\,O and moves with constant velocity (8i−4j)(8\mathbf{i} - 4\mathbf{j})(8i−4j) km h−1\text{h}^{-1}h−1. Another boat B B\,B has position vector (32i−29j)(32\mathbf{i} - 29\mathbf{j})(32i−29j) km relative to a fixed origin O O\,O and moves with constant velocity (−12i+12j)(-12\mathbf{i} + 12\mathbf{j})(−12i+12j) km h−1\text{h}^{-1}h−1.
Show that if both boats maintain their course and speed, they will collide and find the time and position vector at which this occurs.
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.