Crossing a river against the current

A river is \(60\) m wide with straight parallel banks running east–west. The current flows due east at \(1.5\) m/s. A boat can move at \(2.5\) m/s relative to the water. Take \(\mathbf i\) as \(1\) m/s due east and \(\mathbf j\) as \(1\) m/s due north, and assume the current is the same across the whole river.

1. The boat is pointed due north. Write down its resultant velocity as a column vector, and find the time taken to cross and how far downstream it lands.[3]
2. The boat is instead pointed so that it travels straight across to the point directly opposite. Find its velocity relative to the water as a column vector, and the time taken to cross.[3]
3. In practice the current is slower near the banks than in the middle. State how this affects your answer to (a).[2]