person walks 5 km north, then turns left and walks 3 km, then turns left again and walks 5 km. How far is he from the starting point?

Appeared in: NORCET 7 Prelims -2024

Explanation

The problem involves calculating the net displacement from a starting point after a series of movements.
The first movement is 5 km North, and the third movement is 5 km South. These are equal and opposite, so they cancel each other out in the vertical direction.
The only remaining displacement is the 3 km walk to the West.
Therefore, the final distance from the starting point is the magnitude of this westward displacement, which is 3 km.

Option A: 10 km is the total distance walked (5 km + 3 km + 5 km), not the displacement from the starting point.
Option B: 8 km is the sum of the first two legs of the journey (5 km + 3 km). It does not account for the final 5 km walk South.
Option C: 5 km represents the length of the North and South legs of the journey, but it is not the final distance from the starting point.

Visual 1: Diagram - A simple diagram showing the path of the person. It would show a starting point, an arrow pointing up labeled '5 km', a left turn with an arrow pointing left labeled '3 km', and another left turn with an arrow pointing down labeled '5 km'. This visually forms a rectangle, making it clear that the distance between the start and end points is 3 km.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of displacement and vector analysis in a real-world scenario as background academic context rather than a clinical decision trigger.
This is a non-clinical question designed to assess logical reasoning and problem-solving skills.
Spatial awareness and the ability to visualize paths and directions are foundational skills that can be useful in various contexts, including navigating a large hospital or understanding anatomical directions.
What if the person turned right instead of left the second time? If the person walked 5 km North, 3 km West, and then turned right to walk 5 km East, they would end up 5 km North and 2 km East of the starting point. The distance would be the hypotenuse of a right triangle: sqrt(5^2 + 2^2) = sqrt(29) km.

How to Approach the Question

Read the question carefully to understand the sequence of movements.
Visualize the path. It's often helpful to draw a simple diagram with arrows representing each movement.
Break down the movements into cardinal directions (North, South, East, West).
Calculate the net movement in the North-South direction and the net movement in the East-West direction.
Recognize that opposite movements (like North and South) cancel each other out.
The final distance from the start (displacement) is the straight-line distance from the starting point to the ending point, which can be found using the net movements.

Concept Tested & Keywords

Concept Tested: This question tests the concept of displacement and vector analysis in a real-world scenario.
Stem keywords: walks, north, turns left, km
Lead-in keywords: How far
Negative lead-in flag: false

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Practise the full NORCET 7 Prelims -2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.