Question

A man walks 10 m south. Then turning to his right, he walks 12 m. Then turning to his left, he walks 8 m. Again, he turns to his left and walks 5 m. How far is he from his initial position?

• A. 373 m
• B. 363 m
• C. 383 m
• D. 353 m

Hint:

Always draw a direction diagram (N, S, E, W) to trace the path. Keep track of coordinate changes to easily use Pythagoras theorem for the final distance.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to calculate the shortest distance between the starting point and the final point after a series of movements.
Step 2: Detailed Explanation:
Let the starting point be at coordinates \((0, 0)\).

Walks 10 m South: Current position is \((0, -10)\).
Turns right and walks 12 m: Facing South, a right turn is towards the West. Move 12 m West. Current position is \((-12, -10)\).
Turns left and walks 8 m: Facing West, a left turn is towards the South. Move 8 m South. Current position is \((-12, -18)\).
Turns left and walks 5 m: Facing South, a left turn is towards the East. Move 5 m East. Current position is \((-12 + 5, -18) = (-7, -18)\).
Now, calculating the distance from the initial position \((0, 0)\) to the final position \((-7, -18)\) using the distance formula: \[ \text{Distance} = \sqrt{(-7 - 0)^2 + (-18 - 0)^2} \] \[ \text{Distance} = \sqrt{(-7)^2 + (-18)^2} \] \[ \text{Distance} = \sqrt{49 + 324} \] \[ \text{Distance} = \sqrt{373} \text{ m} \] Step 3: Final Answer:
Based on the calculation, the value related to the distance is 373.