Boat problem

A river flows due West at a speed of 2.5 metres per second and has a constant width of 1 km. You want to cross the river from point A (South) to a point B (North) directly opposite with a motor boat that can manage to a speed of 5 metres per second. a) If you head out pointing your boat at an angle of 90 degrees to the bank. How long does it take to cross the river? After reaching the bank, how far will the boat be from point B? Use the following simulation to observe and analyse the motion of the boat under the given conditions. Click the Start button to activate the motion of the boat. Click the Reset button to put the boat back to its original position.

b) In what direction should you point your motor boat in order to travel directly from point A to point B? How long does it take in such case? Use the above simulation to help you answer the questions. Change the direction of the boat to find an approximate solution. Then find the solution and check your answer in the simulation.