In this question, the \(x\)- and \(y\)-directions are east and north respectively. The units are metres and seconds.

Boat \(A\) starts from the origin \(O\) and moves with constant speed \(5\sqrt3\text{ m s}^{-1}\) on a bearing of \(030^\circ\).

After \(100\) seconds boat \(B\) starts from point \(P\), which has position vector \(\binom{0}{1000}\). Boat \(B\) moves with constant speed \(10\text{ m s}^{-1}\) on a bearing of \(060^\circ\).

(a) Find the velocity of each boat in vector form.

(b) Show that the two boats will collide.