At 09:00 hiker A A\,A has position vector (6i−2j)(6\mathbf{i} - 2\mathbf{j})(6i−2j) km and moves with constant velocity (−2i+4j)(-2\mathbf{i} + 4\mathbf{j})(−2i+4j) km h−1\text{h}^{-1}h−1. Hiker B B\,B has position vector (11i+3j)(11\mathbf{i} + 3\mathbf{j})(11i+3j) km and moves with constant velocity (2i+2j)(2\mathbf{i} + 2\mathbf{j})(2i+2j) km h−1\text{h}^{-1}h−1.
Find the relative displacement of hiker A A\,A from hiker B B\,B after t t\,t hours.
Find the time when A A\,A is due west of BBB.
Find the time, after 09:00, when the hikers are exactly 290 \sqrt{290}\,290 km apart.
Practise Edexcel A Level Maths Further Kinematics with exam-style questions for A Level Maths. 54 questions covering Vectors in Kinematics, Vector Methods with Projectiles, Variable Acceleration in One Dimension, Differentiating Vectors, and Integrating Vectors, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.