Problem
Learning Objectives: After successful completion of this assignment, students will be able to
• Resolve a 2D vector into components and find the magnitude of the vector.
• Perform algebraic operations on vectors, including addition, subtraction, and scalar multiplication.
• Convert between vector representations.
Problem Statement: You've discovered part of an old pirate map, directing you to buried treasure somewhere in the woods by the coast. The map tells you to start at the large oak tree, go 1.5 miles at an angle 30° north of east, then continue due east for another 1 mile.
1. You find the oak tree and head out at an angle north of east, walking at 3 miles per hour. Unfortunately, after walking for 15 minutes, you realize you got your compass flipped around and were actually heading south of east! Not wanting to waste time backtracking, you decide to try and head directly for the treasure. Draw an accurate vector diagram showing the position of the oak tree, the destination and your current position. Draw and label the vector from your current position to the treasure.
2. Using your diagram, what should your new heading be in degrees north of east from your curent position? and how far should you walk?
3. At the location indicated, you find a second piece of the map. It says to "follow the first leg twice more and reverse the second leg thrice more." You interpret this to mean that the next location is 2 times the first vector you traversed and -3 times the second vector. Add this location to your vector diagram. How far away is this location from the starting tree?
4. At the next location, you find the third and final piece of the treasure map. It tells you that the treasure is buried at 8000 paces east and 2000 paces north of the starting tree. Conveniently, a note at the bottom of the map indicates that you are currently at 3800 paces east and 4500 paces north. How far do you need to walk and with what heading to get to the buried treasure? Add the final location to your diagram.
5. It turns out that a group of bandits has been spying on your every move. Right as you set out toward the treasure, the bandits head to that location from the tree. If they're also moving at 3 miles/hour, how fast do you need to go to beat them to the treasure?