A man walks 5m towards east then he moves 4m towards south then he moves 3m towards west again moves 2m towards north at last moved 1m towards west.find the distance and displacement
resultant N direction: -4m+2m=-2m or 2m S
resultant E direction: 4m-3m-1m=0m
displacement is result, or 2mS
distance is 4+3+2+1=10m
To find the distance and displacement of the man's movement, we can plot the movements on a coordinate plane. Let's assume the starting point is the origin (0, 0).
1. The man walks 5m towards the east: This means he moves 5 units to the right on the x-axis, ending up at the point (5, 0).
2. Then, the man moves 4m towards the south: This means he moves 4 units downwards on the y-axis, ending up at the point (5, -4).
3. Next, the man moves 3m towards the west: This means he moves 3 units to the left on the x-axis, ending up at the point (2, -4).
4. After that, the man moves 2m towards the north: This means he moves 2 units upwards on the y-axis, ending up at the point (2, -2).
5. Finally, the man moves 1m towards the west: This means he moves 1 unit to the left on the x-axis, ending up at the point (1, -2).
Now, let's calculate the distance and displacement:
Distance:
To calculate the distance traveled, we sum up the individual distances traveled in each direction:
Distance = Total distance traveled in the x-axis + Total distance traveled in the y-axis
In this case, the total distance traveled in the x-axis is 5 + 3 + 1 = 9m
The total distance traveled in the y-axis is 4 + 2 = 6m
Distance = 9m + 6m = 15m
Therefore, the total distance traveled by the man is 15 meters.
Displacement:
To calculate the displacement, we measure the straight-line distance from the starting point to the final point. This is the shortest distance between the two points.
Using the distance formula, we can calculate the displacement:
Displacement = √[(final x - initial x)² + (final y - initial y)²]
In this case, the initial point is (0, 0), and the final point is (1, -2):
Displacement = √[(1 - 0)² + (-2 - 0)²]
Displacement = √[1 + 4]
Displacement = √5
Therefore, the displacement of the man is √5 meters.