Goal: To find the total distance and displacement vector to your house from ETHS!
Here is the question for you – how can you determine the total distance you walk from ETHS to your house, as well as the displacement vector from ETHS to your house? Think about what information you need to find these, and how can you use Google Maps to help. ETHS is 1600 Dodge Avenue.
On graph paper, make a map (to scale) from ETHS to your house and use data from Google Maps to get the total distance and displacement vector. These will all be different for each person in class. Be sure to define your scale, such as 1 cm on the map is equal to 100 feet, or whatever you want it to be for your map. Also orient your map with N, S, E, W, so you can calculate the angle of the displacement vector from ETHS to your home! Give your angle in terms of how many degrees from 0-degrees, which is the positive x-axis. Let ETHS be the origin of your graph.
1. In your own words, what is the distinction between ‘distance’ and ‘displacement?’
2. Write down your results for distance and displacement vector measurements from your map. You’ll need the total x- component (along East-West axis) total y-component (along the North-South axis) of your displacement vector, as well as the direction (i.e. angle) of the displacement vector from ETHS to your house. Express the results in feet, meters and miles. 1 mile = 5280 feet = 1609.3 meters
3. Can the magnitude of displacement ever have a larger magnitude than distance? Explain.
4. Explain how displacement vectors would be used in the navigation of ships or planes.
5. What about global travel – motion over a 3-D surface – does anything change? If so, what new variables do you need to consider? Explain any thoughts on this (talk it through with others if you wish). Think of the Sphereland movie.
Bonus: How do space scientists and engineers navigate space probes that are sent to other objects in the solar system? For instance, what navigation issues and considerations come up with sending people to Mars?