Study the following information carefully and answer the given questions. Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a specific direction, and covers a certain distance before reaching its final position which is named as ship's captain's name. Movements of the ships: I. Ship A, steered by Captain P, starts moving north and covers 5m, then turns left and moves 8m, finally turning right and moving 10m to reach its final position. II. Ship B, steered by Captain Q, moves east for 12m, then turns right and moves 7m, finally turning right again and moving 3m to its final position. III. Ship C, steered by Captain R, starts by moving south for 6m, then turns right and moves 5m, then turns left and moves 9m to its final position. IV. Ship D, steered by Captain S, moves west for 10m, then turns left and moves 4m, finally turning right and moving 6m to its final position. V. Ship E, steered by Captain T, starts moving north for 8m, then turns right and moves 10m, finally turning right again and moving 5m to its final position. What is the shortest distance between the initial and final position of ship B?
Verbal Reasoning
Direction Sense Test
Difficulty: Medium
Choose an option
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A130 m
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B$\sqrt{100}$ m
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C120 m
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D$\sqrt{130}$ m
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ENone of these
Answer
Correct Answer: $\sqrt{130}$ m
Explanation
### Concept & Pythagorean Theorem
The shortest distance between two points on a 2D plane (initial and final position) is calculated using the distance formula or Pythagorean theorem: $\text{Distance} = \sqrt{\Delta x^2 + \Delta y^2}$.
### Step-by-Step Solution
* **Find initial position:** The starting dock is the origin $(0, 0)$.
* **Find final position of Ship B (Q):** It moves east 12m to $(12, 0)$, turns right (south) 7m to $(12, -7)$, and turns right (west) 3m to $(9, -7)$.
* **Calculate shortest distance:** The displacement in the x-direction is 9m (East) and in the y-direction is -7m (South).
* Using Pythagoras: $\text{Distance} = \sqrt{9^2 + (-7)^2} = \sqrt{81 + 49} = \sqrt{130}\text{ m}$.
### Exam Strategy & Shortcut
Break the movement into net horizontal and vertical components. Net East = $12 - 3 = 9$. Net South = 7. The shortest distance is simply the hypotenuse of a right triangle with legs 9 and 7.
### Common Pitfall
Simply adding the segments ($12 + 7 + 3$) instead of finding the straight-line displacement.
### Final Answer
Therefore, the correct answer is **$\sqrt{130}$ m**.