Introduction/Background Ancient sea captains used dead reckoning to keep their ships on course throughout their voyages and figure out where they were going. Do you think that they followed the sun, the shoreline or even the stars.7 Yes, they did. However, by knowmg the speed, time, and course of their travel, they could determine where and approximately when they would arrive. Columbusand most other sailors of his eraused dead reckoning to navigate. Starting from a known point, such as a port, a navigator measures out the course and distance from that point on a chart, pricking the chart with a pin to mark the new position. These early navigators used math to help them find theirwayand stay on course when wind, current and other factors affected theirjourneys. Unfortunately, Columbus never reached the destination where he thought he would end up. Why do you think that happened? Dead reckoning is the process of navigation by advancing a known position using course, speed, time, and distance to he traveled. In other words, figuring out where you will be at a certain time if you hold the speed, time, and course you plan to travel. ,ai JW\" m Figure 1. Graphical illustration of a vessel's voyage using vectors. The course is the direction you intend to steer the vessel. For this exercise, the "course" is always due west. The track that is actually followed can be very crooked due to wave action, current, wind, and the person responsible for steering the vessel. The "course made good" is the course that was actually traveled. Vectors give us a graphical method to calculate the sum of several simultaneous movements. If movement 'is affected by only one variable (represented by vector A or B), then a vessel would arrive at the end of that vector. If movement is affected by two variables (represented by the sum of A and B), then a vessel's final position can be found by linking the two vectors together. Figure 2. Vectors illustrate the final position of vessel's voyage. Follow the assignment instructions and review the rubric: Instructions General information: ' Your ship can sail 6 squares/month. Each square represents 125 miles. 0 Use the attached worksheet to chart each of the three courses as part of this project. I You should also include a separate document that details all of your work and answers to the questions in Parts 175. I have attached a sample document you can use for this, oryou can create your own. Part 1: Starting from Portugal at the blue star and traveling due west, draw one vector for each month of travel, connecting them tip to tail until you reach land. I In what countw will you make landfall? I How many months will it take to reach land? Part2: Unfortunately, the wind does not always blow the way you want! To determine how the wind affects our travel we will have to include the wind vector. First, draw your ship vector, just like' In part 1 Now at the end of that vector, add the wind vector. . > Please label each ship vector and wind vector as snumber and wnumber respectively. Now, draw the resulting vector, and label that as rnumber. For example, the rst shipvector, wind vector, and resultant vector will be named :1 ml, and r1. the same for the next month and each subsequent month until you reach land. Remember that the wind changes, so each month you will have to add a different wind vector. The list of different winds for each month' Is on the following line. 0 Month 1: 3 squares S 0 Month 2:2 diagonal squares SE 0 Month 3: 4 squares W 0 Month 4: 3 diagonal squares SW 0 Month 5:6 squares S 0 Where will you make landfall now? 0 How many months to reach land? Part 3: Calculate the actual total distance traveled by the ship on the way to your destination in Part 2. The actual distance traveled by the ship is sum of the resultant vectors for each month. Give your answer in miles, rounded to the nearest whole number. Part 4: Calculate the speed of the ship in both miles per month and miles per hour (rate = distance/time). Assume 31 days/month. Give youranswers rounded to the nearest whole numbers. Part 5: Sail from your destination in Part 2 to the red star located on the African coast. Travel the same 6 squares each month. Plot your own course adding in wind vectors. Your course must include a minimum of 3 wind vectors that are different directions. Please write down the directions ofyourwind vectors as part ofyour work for this part. Then calculate the total distance in miles and speed of the ship in miles per month and miles per hour. \fPart 1: In what country will you make landfall? How many months will it take to reach land? Part 2: Where will you make landfall now? How many months to reach land? Part 3: What is the actual total distance traveled by the ship on the way to its destination in Part 2? Give your answer in miles, rounded to the nearest whole number. Part 4: What is the speed of the ship in both miles per month and miles per hour? (HINT: rate = distance/time) Assume 31 days/month. Give your answers rounded to the nearest whole numbers. Part 5: List the wind vectors used with their directions on your course to Africa. What is the total distance in miles for this voyage