A man can row a boat at \(3\text{ m s}^{-1}\) in still water. He wants to cross a river from \(A\) to \(B\), where \(AB\) is perpendicular to both banks. The river is \(50\text{ m}\) wide and flows at \(1\text{ m s}^{-1}\). The man points his boat at an angle \(\alpha^\circ\) to the bank.

(i) Find \(\alpha\).

(ii) Find the resultant speed of the boat from \(A\) to \(B\).

(iii) Find the time taken to travel from \(A\) to \(B\).

On another occasion the man points the boat in the same direction, but the river speed is \(1.8\text{ m s}^{-1}\), so he lands at \(C\).

(iv) State the time taken to travel from \(A\) to \(C\), and hence find \(BC\).