The Ferrymans Problem

When a boat is crossing a river, the boat cannot just point itself at the point opposite and expect to go there. Water is flowing downstream and will carry the boat along with it. If the boat is able to travel at a speedm/s in still water and the river is flowing at a speedm/s then for each m the boat moves towards the opposite bank, it will be carriedm downstream. The direction of the water flow is at right angles to the direction the boat needs to travel and the direction of travel of the boat will be at an angleto the intended path:

The boat can be made to travel directly opposite the river to the point on the bank opposite the start point by pointing the nose of the boat against the water flow. The nose of the boat must be pointed into the stream. The boat still travels at a speedthrough the water butis now the hypotenuse of the right angled triangle.

The boat must point its bow to travel at an angleto the intended path.

The effective speed of the boat is reduced fromtom/s and the boat must also burn more fuel since it has to travel longer through the water.

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