7. [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A ship \(S\) is moving along a straight line with constant velocity. At time \(t\) hours the position vector of \(S\) is \(\mathbf { s } \mathrm { km }\). When \(t = 0 , \mathbf { s } = 9 \mathbf { i } - 6 \mathbf { j }\). When \(t = 4 , \mathbf { s } = 21 \mathbf { i } + 10 \mathbf { j }\). Find

1. the speed of \(S\),
2. the direction in which \(S\) is moving, giving your answer as a bearing.
3. Show that \(\mathbf { s } = ( 3 t + 9 ) \mathbf { i } + ( 4 t - 6 ) \mathbf { j }\). A lighthouse \(L\) is located at the point with position vector \(( 18 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\). When \(t = T\), the ship \(S\) is 10 km from \(L\).
4. Find the possible values of \(T\).