Final answer:
The boy has traveled a total distance of 7 km, and his resultant displacement, calculated using the Pythagorean theorem, is 5 km.
Step-by-step explanation:
The question you've asked pertains to distance and displacement in the context of a two-dimensional plane. When a boy travels 3 km north and then 4 km east, we can use the Pythagorean theorem to determine the total distance he has traveled. The northward and eastward travels can be considered as two sides of a right-angled triangle, where traveling north represents one side, traveling east represents the other, and the hypotenuse would be the resultant displacement.
To find the total distance, we simply add the two distances traveled in the two directions together:
- Distance traveled north = 3 km
- Distance traveled east = 4 km
- Total distance traveled = 3 km + 4 km = 7 km
The resultant displacement, which is the straight-line distance from the starting point to the final position, can be calculated using the Pythagorean theorem, which is:
√(3² + 4²) = √(9 + 16) = √25 = 5 km
Therefore, the total distance traveled by the boy is 7 km and the resultant displacement is 5 km.