[In this question the unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and north respectively]
A ship S S\,S is moving with constant velocity (−2.5i+6j) km h−1(-2.5\mathbf{i} + 6\mathbf{j}) \text{ km h}^{-1}(−2.5i+6j) km h−1. At time 1200, the position vector of S S\,S relative to a fixed origin O O\,O is (16i+5j) km(16\mathbf{i} + 5\mathbf{j}) \text{ km}(16i+5j) km.
Find the speed of SSS.
Find the bearing on which S S\,S is moving.
The ship is heading directly towards a submerged rock RRR. A radar tracking station calculates that, if S S\,S continues on the same course with the same speed, it will hit R R\,R at the time 1500. Find the position vector of RRR.
The tracking station warns the ship's captain of the situation. The captain maintains S S\,S on its course with the same speed until the time is 1400. He then changes course so that S S\,S moves due north at a constant speed of 5 km h−1^{-1}−1. Assuming that S S\,S continues to move with this new constant velocity, find an expression for the position vector of the ship t t\,t hours after 1400.
Find the time when S S\,S will be due east of RRR.
Find the distance of S S\,S from R R\,R at the time 1600.
9 exam-style questions on Edexcel A Level Old Maths Vectors. Each one has a worked solution and a mark scheme showing where the marks go.