At 6 a.m. a boat A A\,A has position vector (8i−7j)(8\mathbf{i} - 7\mathbf{j})(8i−7j) km relative to a fixed origin O O\,O and moves with constant velocity (6i−4j)(6\mathbf{i} - 4\mathbf{j})(6i−4j) km h−1^{-1}−1. Another boat B B\,B has position vector (29i−28j)(29\mathbf{i} - 28\mathbf{j})(29i−28j) km relative to a fixed origin O O\,O and moves with constant velocity (−8i+10j)(-8\mathbf{i} + 10\mathbf{j})(−8i+10j) km h−1^{-1}−1.
Find expressions for the position vectors of A A\,A and BBB, in terms of t t\,t hours after 6 a.m.
Show that if both boats maintain their course and speed, they will collide and find the time and position vector at which this occurs.
At 7 a.m. boat A A\,A realises that a collision is imminent and changes course so that it now has velocity (−9i+16j)(-9\mathbf{i} + 16\mathbf{j})(−9i+16j) km h−1^{-1}−1. Find the distance between the two ships at the time when they would have collided.
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.