At 10 a.m. plane A A\,A has position vector (3i−j)(3\mathbf{i} - \mathbf{j})(3i−j) km and moves with constant velocity (2i+2j)(2\mathbf{i} + 2\mathbf{j})(2i+2j) km h−1\text{h}^{-1}h−1. Another plane B B\,B has position vector (4i+j)(4\mathbf{i} + \mathbf{j})(4i+j) km and moves with constant velocity (3i+j)(3\mathbf{i} + \mathbf{j})(3i+j) km h−1\text{h}^{-1}h−1.
Find the position vector of plane A A\,A after t t\,t hours.
Find the position vector of plane B B\,B after t t\,t hours.
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 3 km apart.
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.