You are going hiking in Brown County State Park this weekend and want to plan your route to Lake
Monroe. Starting from the parking lot, you plan on hiking 2300 m due west, 17500 m due south, 1900 m due
east, and 1200 m due north. What will be the total distance of your hike if you take this route? What will be
your resultant displacement from the parking lot to your ending position at Lake Monroe, relative to the right
horizontal from your final position?
total distance is just the sum of all the separate pieces. I'm sure you can add them up.
For the final location, just add up the separate displacements (in 100's of meters).
(0,0) to (-23,0) to (-23,-175) to (-4,-175) to (-4,-163)
Now you can figure the east-west, north-south, and total displacements.
Okay thanks, but how would you then calculate the total displacement from there? Sorry I am just a bit lost.
just use your usual distance formula. The final displacement is just
100*√(4^2+163^2) = 100√26585 = 16305m
To calculate the total distance of your hike, you will need to add up the distances covered in each direction.
1. Distance hiking due west: 2300 m
2. Distance hiking due south: 17500 m
3. Distance hiking due east: 1900 m
4. Distance hiking due north: 1200 m
Adding these distances together:
Total distance = 2300 m + 17500 m + 1900 m + 1200 m
Total distance = 22,900 m
Therefore, the total distance of your hike will be 22,900 meters.
Now, let's calculate the resultant displacement. To do this, we need to find the vector sum of the individual displacements.
1. Displacement due west: 2300 m
2. Displacement due south: 17500 m
3. Displacement due east: 1900 m
4. Displacement due north: 1200 m
To simplify the calculation, we can convert these displacements into a two-dimensional coordinate system. We'll consider east to be the positive x-direction and north to be the positive y-direction.
The sum of displacements in the x-direction (east - west) is: 1900 m - 2300 m = -400 m (negative because it's westward).
The sum of displacements in the y-direction (north - south) is: 1200 m - 17500 m = -16300 m (negative because it's southward).
Therefore, the resultant displacement, relative to the right horizontal from your final position, is (-400 m, -16300 m).
To find the magnitude of this resultant displacement, you can use the Pythagorean theorem:
Magnitude = sqrt((-400 m)^2 + (-16300 m)^2)
Magnitude ≈ 16,412.1 m
So, the resultant displacement from the parking lot to Lake Monroe is approximately 16,412.1 meters, relative to the right horizontal from your final position.