A treasure map instructs you to walk 34 m south, 117 m east, followed by 64.5 m north, and finally 28.5 east. Determine the magnitude of your total displacement in m.
Disp. = -34i + 117 + 64.5i + 28.5 = 145.5 + 30.5i.
Magnitude = sqrt(145.5^2+30.5^2) =
To determine the magnitude of your total displacement, we need to calculate the net displacement vector.
1. Start by creating a coordinate system with north being the positive y-direction and east being the positive x-direction.
2. Begin by drawing a vector 34 m long pointing straight down, representing the 34 m south.
3. Next, draw a vector 117 m long pointing to the right, representing the 117 m east.
4. Now, draw a vector 64.5 m long pointing straight up, representing the 64.5 m north.
5. Finally, draw a vector 28.5 m long pointing to the right, representing the 28.5 m east.
6. Add up all the vectors to get the net displacement vector by connecting the initial point of the first vector to the final point of the last vector.
7. Measure the magnitude, or length, of the net displacement vector in meters to determine the answer.
By following these steps, you can find the magnitude of your total displacement.