Understanding the Movement
The person moves in three distinct segments:
- 20 m North: This sets the initial position.
- 30 m East: This adds to the eastward displacement.
- 40√2 m South West: This segment combines south and west movements.
Breaking Down the Final Movement
To analyze the 40√2 m movement towards the southwest:
- The southwest direction implies a 45-degree angle south of west, which can be resolved into two components:
- South Component: 40√2 * sin(45°) = 40 m
- West Component: 40√2 * cos(45°) = 40 m
This means the person effectively moves 40 m South and 40 m West.
Calculating the Net Displacement
Now, let's sum up the movements in each direction:
- North-South Movement:
- Total North = 20 m
- Total South = 40 m
- Net South = 40 m - 20 m = 20 m South
- East-West Movement:
- Total East = 30 m
- Total West = 40 m
- Net West = 40 m - 30 m = 10 m West
Resultant Displacement
To find the resultant displacement, we use the Pythagorean theorem:
- Distance = √(South^2 + West^2)
- Distance = √(20^2 + 10^2) = √(400 + 100) = √500 = 10√5 m
Direction of the Displacement
To find the angle θ with respect to the south:
- θ = tan⁻¹(Opposite/Adjacent) = tan⁻¹(10/20) = tan⁻¹(0.5)
This results in a displacement of 10√5 m at an angle θ south of west.
Thus, the final displacement of the person is 10√5 m at an angle south of west.