2026 IGCSE Additional Mathematics May/June 0606/22 Q7

In this question, \(\mathbf i\) is a unit vector due east and \(\mathbf j\) is a unit vector due north.

Distances are measured in kilometres and time is measured in hours.

Point \(P\) has position vector \(2\mathbf i+5\mathbf j\) relative to an origin \(O\).

At \(13\,00\), boat \(A\) sails from point \(P\) with velocity vector \(8\mathbf i+8\mathbf j\).

1. Find the position vector of \(A\) at the end of 2 hours of sailing.[1]
2. Write down the position vector of \(A\) at the end of \(t\) hours of sailing.[1]
3. Point \(Q\) has position vector \(20\mathbf i+8\mathbf j\) relative to the origin \(O\).
   At \(15\,00\), boat \(B\) sails from point \(Q\) on a bearing of \(300^\circ\) with a constant speed of \(5\sqrt3\).
   Find the position vector of \(B\) at \(17\,00\).[3]
4. Find the distance between the two boats at \(17\,00\).[3]