a boy travels a distance of 10m towards south and then he runs towards east and travels 12m in that direction calculate:
i)total distance covered by the boy
ii)displacement from his initial position
10+12
√(10^2+12^2)
To calculate the total distance covered by the boy, you can use the concept of vector addition.
First, visualize the boy's movement on a coordinate plane. Let's assume the starting point is the origin (0,0), and the positive X-axis represents east, while the positive Y-axis represents north.
i) To calculate the total distance covered by the boy, we need to find the sum of the magnitudes of both the South and East distances. Since the boy covers 10m towards the south and then 12m towards the east, the total distance covered is:
Total distance = South distance + East distance
= 10m + 12m
= 22m
Therefore, the total distance covered by the boy is 22 meters.
ii) To calculate the displacement from the boy's initial position, we need to find the straight-line distance between his final position and the initial position.
We can find the displacement using the Pythagorean theorem. The straight-line distance is the hypotenuse of a right-angled triangle formed by the south and east distances.
Displacement = √(South distance^2 + East distance^2)
= √(10m^2 + 12m^2)
= √(100m^2 + 144m^2)
= √(244m^2)
= √244m
Therefore, the displacement from the boy's initial position is approximately 15.62 meters (rounded to two decimal places).