Distance:
To calculate the distance traveled by the person, we need to consider the total path length covered. The person moves northwards by 20 m, then eastwards by 30 m, and finally westwards by 40 m.

1. Northwards movement: The person moves 20 m northwards.
2. Eastwards movement: The person moves 30 m eastwards.
3. Westwards movement: The person moves 40 m westwards.

To find the total distance traveled, we need to add the magnitudes of the individual movements:
Distance = 20 m + 30 m + 40 m = 90 m

So, the person has traveled a distance of 90 meters.

Magnitude of Displacement:
The magnitude of displacement is the shortest distance between the initial and final positions, irrespective of the path taken.

1. Northwards movement: The person moves 20 m northwards.
2. Eastwards movement: The person moves 30 m eastwards.
3. Westwards movement: The person moves 40 m westwards.

To determine the displacement, we need to consider the net effect of these movements. Since the person moves northwards and then eastwards before finally moving westwards, we can visualize the movements as follows:

North 20 m
/
/
/
/
/
/
/
/------------------------------------ West 40 m
\
\
\
\
\
\
\
East 30 m

To find the magnitude of displacement, we need to calculate the distance between the starting point and the endpoint of the person's journey. In this case, the starting point and endpoint are the same.

Using Pythagoras' theorem, we can calculate the displacement as follows:

Displacement = √[(20 m)^2 + (30 m - 40 m)^2]
= √[(20 m)^2 + (-10 m)^2]
= √[400 m^2 + 100 m^2]
= √500 m^2
= 22.36 m (rounded to two decimal places)

Therefore, the magnitude of the displacement is approximately 22.36 meters.

Solution