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

this is a right triangle

distance is how far he ran 10 + 12 = 22 m
displacement is how far he is from the start and is a vector so also has direction.
how far from start = hypotenuse = sqrt (100 + 144) = 15.6 m
tangent of angle south of east = 10/12
angle south of east = 39.8 degrees
If using a compass angle clockwise from north = 90 + 39.8

A ball is thrown vartically upward it rises upto a height of 10 m,and comes back to the initial position.calculate:

1.the total distance covered by the ball
2. that displacement of the ball

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

(i) Total Distance:

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

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

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

(ii) Displacement:

Displacement is the straight line distance between the initial position and the final position. We can find it using Pythagoras theorem.

Distance travelled towards south = 10 m
Distance travelled towards east = 12 m

Using Pythagoras theorem,

Displacement = √(Distance towards south^2 + Distance towards east^2)
Displacement = √(10^2 + 12^2)
Displacement = √(100 + 144)
Displacement = √244
Displacement ≈ 15.62 m

Therefore, the displacement from the boy's initial position is approximately 15.62 meters.

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

(i) Total Distance Traveled:
The boy travels 10 m south and then 12 m east. Since these distances are perpendicular, we can use the Pythagorean theorem to find the total distance.

Using the formula c^2 = a^2 + b^2, where c is the hypotenuse (total distance), and a and b are the two perpendicular distances:

c^2 = (10^2) + (12^2)
c^2 = 100 + 144
c^2 = 244

Taking the square root of both sides, we get:
c = √244
c ≈ 15.62 m

So, the total distance traveled by the boy is approximately 15.62 meters.

(ii) Displacement from the Initial Position:
The displacement is the shortest distance between the initial and final positions. This can be found using the Pythagorean theorem as well, but using the differences in distances traveled in each direction.

To find the displacement, we calculate the horizontal and vertical components of the positions and then combine them to find the resultant displacement.

The horizontal distance traveled towards the east is 12 m. Since the boy did not travel towards the west, the horizontal component of the displacement is 12 m.

The vertical distance traveled towards the south is 10 m. Since the boy did not travel towards the north, the vertical component of the displacement is -10 m (negative because it is in the opposite direction).

Using the Pythagorean theorem on the horizontal and vertical components:

x^2 = (12^2) + (-10^2)
x^2 = 144 + 100
x^2 = 244

Taking the square root of both sides, we get:
x = √244
x ≈ 15.62 m

The displacement from the initial position is approximately 15.62 meters.

So, (i) the total distance traveled by the boy is approximately 15.62 meters, and (ii) the displacement from his initial position is approximately 15.62 meters.