At 10 a.m. plane A A\,A has position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) km and moves with constant velocity (−4i+6j)(-4\mathbf{i} + 6\mathbf{j})(−4i+6j) km h−1\text{h}^{-1}h−1. Another plane B B\,B has position vector (−3i−9j)(-3\mathbf{i} - 9\mathbf{j})(−3i−9j) km and moves with constant velocity (i+8j)(\mathbf{i} + 8\mathbf{j})(i+8j) km h−1\text{h}^{-1}h−1.
Find the relative displacement of plane A A\,A from plane B B\,B after t t\,t hours.
Find the time when A A\,A is due west of BBB
Find the time, after 10 a.m. when the planes are exactly k k\,k km apart, where k>7k>7k>7.
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.