You are piloting a boat on a river of width L that is moving at a speed vC relative to a pier anchored to the shore. a) Your first goal is to pilot the boat to a target directly across the river, but your boat’s speed controls are damaged so that your boat’s speed relative to the water is fixed at vB = 3vC. At what upstream angle q should you set your boat’s heading in order to reach your target?
b) Having succeeded at your first task, you are given a more difficult one. Your boat’s speed controls are still stuck at vB = 3vC , but this time your heading control is also damaged and points directly across the river. At what downstream angle q will you end up traveling?
c) After some repairs to your boat, you are given one final task. You are to cross the river directly to a target which is at an angle f upstream, but your heading controls are once again stuck pointing at an angle q upstream from your target. What speed should you set for your boat so that you hit your target? Express your answer in terms of vC, q, and f. You may need to use