At 10 a.m. plane A A\,A has position vector (2i−j)(2\boldsymbol{i} - \boldsymbol{j})(2i−j) km and moves with constant velocity (−2i+2j)(-2\boldsymbol{i} + 2\boldsymbol{j})(−2i+2j) km h−1^{-1}−1. Another plane B B\,B has position vector (i−3j)(\boldsymbol{i} - 3\boldsymbol{j})(i−3j) km and moves with constant velocity (i+3j)(\boldsymbol{i} + 3\boldsymbol{j})(i+3j) km h−1^{-1}−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 5 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.