a boy walks 1km due east and then 1km due north.what is his displacement
To find the displacement of the boy, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the boy walks 1km east and then 1km north. We can consider these two distances as the legs of a right-angled triangle. The displacement, which can be considered as the hypotenuse, can be found using the Pythagorean theorem.
Let's calculate it step by step:
Step 1: Square the distances traveled in each direction.
- 1km east squared = (1 km)^2 = 1 km^2
- 1km north squared = (1 km)^2 = 1 km^2
Step 2: Add the squared distances together.
- 1 km^2 + 1 km^2 = 2 km^2
Step 3: Take the square root of the sum to find the length of the displacement.
- Square root of 2 km^2 ≈ 1.41 km
Therefore, the displacement of the boy is approximately 1.41 kilometers.