6. A ship \(A\) has maximum speed \(30 \mathrm {~km} \mathrm {~h} ^ { - 1 }\). At time \(t = 0 , A\) is 70 km due west of \(B\) which is moving at a constant speed of \(36 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) on a bearing of \(300 ^ { \circ }\). Ship \(A\) moves on a straight course at a constant speed and intercepts \(B\). The course of \(A\) makes an angle \(\theta\) with due north.

1. Show that \(- \arctan \frac { 4 } { 3 } \leq \theta \leq \arctan \frac { 4 } { 3 }\).
2. Find the least time for \(A\) to intercept \(B\).
   (5)