Final answer:
To find the distance from the starting point after the four legs of the hike, we need to calculate the total displacement of the hiker by summing the vector displacements of the four legs. The correct answer is B.
Step-by-step explanation:
In order to find the distance from the starting point after the four legs of the hike, we need to calculate the total displacement of the hiker. Displacement is the straight-line distance between the starting and ending points, regardless of the path taken.
Since the hiker makes four straight-line walks in random directions and lengths, we can think of each leg as a vector that represents the displacement. The total displacement is the vector sum of these four legs.
Without knowing the lengths and directions of the legs, we cannot determine the exact distance from the starting point. Therefore, none of the given options (a) 10 km, (b) 20 km, (c) 25 km, or (d) 31 km, can be confidently chosen as the correct answer.
The distance from the starting point after a hike with four straight-line walks in random directions and lengths cannot be determined without the specific lengths and directions of the walks. The problem relates to the concepts of displacement and vector sum.
To determine the distance from the starting point after a hike involving straight-line walks in random directions and lengths, we need to approach the problem with vector addition, as the paths taken can be represented as vectors. Specifically, the scenario is analogous to problems involving displacement and vector sum. Without specific lengths and directions of the four legs of the hike, it is impossible to provide an exact answer. Each leg of the hike would contribute to the total displacement vector, but without information on the directions and lengths of each leg, no numerical answer can be deduced. However, the question references different examples that illustrate how to calculate displacement and distance resulting from vector addition.
For example, if a person walks 18.0 m west and then 25.0 m north, the total displacement is the vector sum of these two legs. The displacement can be calculated using the Pythagorean theorem, resulting in a straight-line distance from the start point. If this was extended to four legs of random directions and lengths, one would use vector addition to find the resultant displacement vector and its magnitude and direction.