Background: Scalars are a type of measurement that most people are familiar with as they quantify a property with only a magnitude such as temperature, length, or weight. Vectors, on the other hand, are a type of measurement that has both a magnitude and a direction. For example, when driving a car from one destination to another, the scalar quantity, distance, represents how far the car drove between the two locations, say 30 kilometers. Meanwhile, the vector quantity, displacement, represents the direct distance between the two locations and the direction of travel, say 30 kilometers in the North-East direction. However, sometimes the measurer cannot easily move directly between the two locations to measure the displacement and direction. In a case such as this one, multiple vectors can be added together to find an overall resultant vector. In order to accomplish this, the individual vectors must first be broken into their x and y components, otherwise known as i-hat and j-hat respectively. The sum of the separated components can then be added, yielding the total components of the resultant vector. The magnitude and direction of the resultant vector can then be calculated using trigonometric functions. 

Methods: 1. We walked between the different sites following straight lines to the North/South and the East/West.

2. The steps were tracked using the fitness feature on an Apple Watch and the distance was recordedin a notebook every time we changed directions.

3. A meter stick was used to measure one step and converted the steps into meters.

4. Common trigonometric functions were used to convert the x and y components into a magnitude and direction.

5. The x and y components for each vector were added to find the resultant vector. 

Discussion: Over the course of this experiment, we determined that the distance from the Roger Statue to the Guardhouse was approximatley 198.94 m at a 121.52 degree angle from East. This was discovered through walking the path shown in the map and counting the amount of steps in the North/South and East/West direction between each location. The steps were then able to be converted into meters and the vectors were added together to determine the overall resultant vector. This technique of using smaller vectors to determine a different resultant vector is applicable to many different circumstances. Not only is it one of the basic skills needed for physics, but the concepts translate to everyday situations such as navigating either in a car or while hiking. 

Errors: After all of the data was collected and we were putting together the map, we noticed that there was a slight problem with one of the distances being logically too short (the distance between the front door of commons and the sidewalk outside of the rec center). To correct for the error, we went back and remeasured that distance to get a more accurate estimate.