Sun 6 Jan, 2013 03:00 pm
A river flows downstream from east to west with a constant speed of 6m/s. There is a boat the usually travels in a straight line between two docks A and B directly opposite each other. The river is straight and has a constant width of 2km. The boat always moves with a speed of 10m/s with respect to the water when it is away from the shore. The captain must calculate the correct angle to aim the boat upstream (measured from straight across so that the combined effect of the boat moving through the water and the water flowing over the land will cause the boat to move due north over the land (or due south on the return trip). One day the captain makes a mistake, he chooses the correct angle described above but aims downstream instead of up and ends up doing diagonally the opposite direction. He stops at land and calculates the correct aiming strategy to retrace the straight line path. How long will this crossing from where he ended up back to the start. Please provide full solution.