A boy travels a distance of 10m towards south and then he runs towards east and travel 12m in that direction. Calculate yhe total distance travelled by the boy and displacement from his initial position.

Distance 22

To calculate the total distance traveled by the boy, we need to find the sum of the distances traveled in each direction.

Distance traveled towards the south = 10m
Distance traveled towards the east = 12m

Total distance traveled = 10m + 12m = 22m

Now, let's calculate the displacement from the boy's initial position. Displacement is a vector quantity that represents the straight-line distance and direction from the initial to the final position.

The boy initially moves towards the south, so we can consider it as the negative y-direction. The distance traveled towards the south is 10m.

The displacement towards the east can be considered as the positive x-direction. The distance traveled towards the east is 12m.

To calculate the displacement, we need to use the Pythagorean theorem to find the distance between the initial and final positions.

Displacement = √((Distance South)^2 + (Distance East)^2)
Displacement = √((10m)^2 + (12m)^2)
Displacement = √(100m^2 + 144m^2)
Displacement = √(100m^2 + 144m^2)
Displacement = √(10000m^2 + 20736m^2)
Displacement = √30736m^2
Displacement ≈ 175.12m (rounded to two decimal places)

Therefore, the total distance traveled by the boy is 22m, and the displacement from his initial position is approximately 175.12m.

To calculate the total distance traveled by the boy, we need to find the sum of the distances traveled in each direction. In this case, the boy travels a distance of 10m towards the south and then 12m towards the east.

Total distance = Distance towards south + Distance towards east
Total distance = 10m + 12m
Total distance = 22m

Therefore, the total distance traveled by the boy is 22 meters.

Now, to calculate the displacement from the boy's initial position, we need to find the shortest straight-line distance between the initial and final positions. We can use the Pythagorean theorem to find the displacement.

Displacement = √(Distance towards south)^2 + (Distance towards east)^2
Displacement = √(10m)^2 + (12m)^2
Displacement = √100m^2 + 144m^2
Displacement = √10000m^2 + 20736m^2
Displacement = √30736m^2
Displacement ≈ 175.14m

Therefore, the displacement from the boy's initial position is approximately 175.14 meters.

Total Distance = sum of distances in each direction (south, then east).

Displacement =
distance between end point and starting point, irrespective of path.
(hint: use Pythagoras theorem, since the two legs are perpendicular to each other).