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^{-1}−1. The relative displacement of plane A A\,A from plane B B\,B after t t\,t hours is (5−5t)i+(4−2t)j(5 - 5t)\mathbf{i} + (4 - 2t)\mathbf{j}(5−5t)i+(4−2t)j km.
Find the position vector of plane B B\,B at 10 a.m. and its constant velocity.
Find the time when A A\,A is due west of BBB
Find the time, after 10 a.m. when the planes are exactly 37 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.