Find the distance traveled and the displacement of the vector.
40 m due north and 30 m due east
6 m due south, 10 m due east, and 5 m due north
20 m to the west, 5 m to the south, and 10 m to the east
To find the distance traveled and the displacement, we'll first break down each vector into its components.
1. 40 m due north and 30 m due east:
- Distance traveled = √(40^2 + 30^2) = √(1600 + 900) = √2500 = 50 m
- Displacement = √((40-0)^2 + (0-30)^2) = √(40^2 + (-30)^2) = √(1600 + 900) = √2500 = 50 m
2. 6 m due south, 10 m due east, and 5 m due north:
- Distance traveled = 6 + 10 + 5 = 21 m
- Displacement = √((0-0)^2 + (-6+5)^2) = √(0^2 + (-1)^2) = √(0 + 1) = √1 = 1 m (displacement is a single value, not a direction or combination of directions)
3. 20 m to the west, 5 m to the south, and 10 m to the east:
- Distance traveled = 20 + 5 + 10 = 35 m
- Displacement = √((-20+10)^2 + (-5)^2) = √((-10)^2 + (-5)^2) = √(100 + 25) = √125 = 11.18 m (rounded to two decimal places)
Note: Distance traveled is the total length of the path covered, while displacement is the straight-line distance between the initial and final positions, regardless of the path taken.