Lab 1: Vectors
Lab 1: Vectors
Embedded Files
Background & Lab Introduction
Background & Lab Introduction
Vectors are a measurement of distance. Vector notation shows distance and direction. For this lab discussing vectors, my peer group and I walked around campus and measured various stops and their distances. We put each stop's details into cartesian coordinates and polar coordinates.
Vectors are a measurement of distance. Vector notation shows distance and direction. For this lab discussing vectors, my peer group and I walked around campus and measured various stops and their distances. We put each stop's details into cartesian coordinates and polar coordinates.
Methods
Methods
We started at the Roger Williams statue. In order, we traveled to the library, global heritage hall, handicap parking spot, the sailing center flagpole, commons, the recreation center, and the guard house. We used the camera app, a distance tracker phone app, and a compass to keep track of the direction. As we went, we wrote down each step we took (direction and distance). After collecting data, we converted our numbers from miles to meters. To find the magnitudes, I had to apply the Pythagorean theorem to the paths. The calculation is a^2+b^2=c^2. Plugging in the sides of the numbers will give the hypotenuse, or magnitude. To find the direction I used inverse trigonometry functions. For each direction calculation, I used arctan (opposite side/adjacent side).
We started at the Roger Williams statue. In order, we traveled to the library, global heritage hall, handicap parking spot, the sailing center flagpole, commons, the recreation center, and the guard house. We used the camera app, a distance tracker phone app, and a compass to keep track of the direction. As we went, we wrote down each step we took (direction and distance). After collecting data, we converted our numbers from miles to meters. To find the magnitudes, I had to apply the Pythagorean theorem to the paths. The calculation is a^2+b^2=c^2. Plugging in the sides of the numbers will give the hypotenuse, or magnitude. To find the direction I used inverse trigonometry functions. For each direction calculation, I used arctan (opposite side/adjacent side).
Roger Statue
Roger Statue
Starting point!
The Library
The Library
Statue to library: +32m î, +32m ĵ
GHH
GHH
Library to GHH: -16m ĵ, +48m î
Handicap Spot
Handicap Spot
GHH to Handicap spot: -8m î, +48m ĵ
Flagpole
Flagpole
Handicap spot to sailing center flagpole: +112m ĵ, +129m Î, -80m ĵ, +32m Î, -24m ĵ (+161m Î, +8m ĵ)
Commons
Commons
Sailing center flagpole to commons: -32m î, +80m ĵ, -145m î (-177m î, +80m ĵ,)
Recreation Center
Recreation Center
Commons to the recreation center: +32m ĵ, -64m î, +32m ĵ (+64m ĵ, -64m î)
Guard House
Guard House
Recreation center to the guard house: -48m ĵ, -80m Î
Visual Map
Visual Map
This is a visual map of the areas we walked. The green icon is the starting point, and the red icon is the end.
Resultants: -88m Î, +168m ĵ
Table 1
Table 1
This table shows the Cartesian and Polar coordinates of the paths we took.
Table 2
Table 2
This table shows the Cartesian coordinates of the paths we took.
Possible Errors: magnitude and direction calculations, distance tracking inaccuracy
Possible Errors: magnitude and direction calculations, distance tracking inaccuracy
Below are two sheets of written out work. It shows the calculation of magnitude and direction.
Results
Results
Overall, this lab was interesting to do. Visualizing the actual distance is helpful. Vectors, magnitude, and direction are more important than I thought. I feel as if I have mastered these calculations through this lab!
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