A man in a maze makes three consecutive displacements. His first displacement is 9 m westward, his second displacement is 7 m northward, and his third displacement is 8 m eastward. How far is he from the starting point?
To find the distance of the man from the starting point, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the man's displacements as the sides of a right-angled triangle. His first and third displacements (9 m westward and 8 m eastward) will cancel each other out because they are in opposite directions. So, we only need to consider his second displacement (7 m northward) as the vertical side of the triangle.
Now, we can calculate the distance of the man from the starting point using the Pythagorean theorem:
Distance^2 = (9 m)^2 + (7 m)^2
Distance^2 = 81 m^2 + 49 m^2
Distance^2 = 130 m^2
Taking the square root of both sides, we find:
Distance = √(130 m^2)
Distance ≈ 11.40 m
Therefore, the man is approximately 11.40 meters away from the starting point.