A motorboat is leaving Island A at 5 knots per hour, and can travel in a straight line to Island B.

• Island A is 25 knots from Island B in a straight line.
• The wind is out of the northwest at 10 knots (45 degrees).
• The current of the water is coming from the south at 2 knots.
  
  

How long will it take the motorrboat to make it to Island B? Explain your answer.

Question 2:

You are taking your sailboat from Island A to Island B, located 45 degrees to the east of north.

Wind conditions prevent you from sailing in a straight line like a motorboat would. Sail boats must change their tack (direction) to take advantage of wind forces. In order to navigate to island B, you will have to perform three separate tacking movements.

• The wind is out of the northwest at 10 knots (45 degrees).
• The current of the water is coming from the south at 2 knots.
• Sail boats can typically travel at 4-7 knots per hour. You can choose the speed of your sail boat. Based on environmental factors, your knots per hour in tack 1 & 3 will be faster than tack 2.

Create three tacks that will carry you from island A to Island B. This will require you to use trigonometry and vectors.

Based on your tacks, how long will it take you to get from Island A to Island B? (Traveling by sail is not a precise science so your time estimate should be in 5 minute increments.).

Hints:

• You should use both trigonometry and vector calculus to solve this problem.
• The islands are 25 knots apart from each other.
• Tacking is sailing in a straight line. Sailors often use multiple tacks to get to their final destination using the wind. For this problem you will have to make three tacks
• You can define the length of your tack and the angle for Tack 1, Tack 2, Tack 3. Each group will likely have a unique answer to this problem.
• You don’t want any of your tacks to be 15 degrees (30 degrees total) on either side of the wind will give you no power in a sailboat.
• You will want to avoid a tack between N 30 west or N 60 degrees west.
• You can’t have a tack angle that is over 180 degrees.