Navigating Through Complex Directions: Solving Rohan's Journey

Have you ever been faced with a complex set of directions that left you questioning the answer? Today, we delve into a problem involving Rohan's journey, where a series of turns and distances lead to an intriguing conclusion.

Understanding the Problem

Rohan follows a series of directions starting from a designated point. Let's explore the journey step-by-step.

Step 1: Rohan walks 3 km to the North.

Step 2: He then turns to his left and walks 5 km to the West. (Since he was facing North and turned left, he now faces West)

Step 3: Rohan again turns to his left and walks 3 km to the South. (Since he was facing West and turned left, he now faces South)

Step 4: He then turns to his left once more and walks 3 km to the East. (Since he was facing South and turned left, he now faces East)

At this point, we need to determine how far Rohan is from his starting point.

Analysis of the Journey

Let's break down the movements on a coordinate plane for clarity:

Step 1: Starting point (0, 0) - After walking 3 km to the North, the new coordinates are (0, 3).Step 2: Turning left (which now means going West), after walking 5 km, the new coordinates are (5, 3).Step 3: Turning left again (now South), after walking 3 km, the new coordinates are (5, 0).Step 4: Finally, turning left once more (which means now East), after walking 3 km, the new coordinates are (2, 0).

Using the coordinate plane, we can see that Rohan ends up 2 km to the West of his starting point.

Conclusion and Additional Insights

The given answer of 3 km is incorrect based on the described journey. Rohan ends 2 km to the West of his starting point, meaning the correct answer is 2 km.

Additional Considerations and Solutions

The problem is designed to be complex and may lead to different interpretations. Here are a few considerations:

Assumption of a Flat Surface: The problem assumes a flat surface for the journey. If it were on a spherical surface, such as the Earth, the answer would be more complex and would depend on the latitude and longitude and Precision: If the directions included specific angles (like 45 degrees), the answer would differ. However, the problem states a 90-degree turn each time, making the solution straightforward.Origin Point: It is assumed the journey starts from a defined point, such as the equator or a specific latitude and longitude. Changing the origin point would alter the coordinates dramatically.

By understanding the journey and breaking down each step, we can accurately determine where Rohan ends up in relation to his starting point.

Summary

Rohan's final position is 2 km to the West of his starting point. This problem demonstrates the importance of careful analysis and understanding of directions and coordinates in navigation and problem-solving.