A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km. Finally, he turns left and walks 3 km. How far is he from the starting point?
Show Hint
- 8.92 km
- 5.89 km
- 7.62 km
- 6.45 km
The Correct Option is C
Solution and Explanation
Step 1: Visualize the movement.
The person starts at the origin, facing north:
1. He walks 8 km north.
2. Turns right (now facing east) and walks 4 km.
3. Turns right again (now facing south) and walks 6 km.
4. Finally, he turns left (now facing east) and walks 3 km.
Step 2: Calculate the final position.
- After walking north for 8 km, he is at (0, 8).
- After walking east for 4 km, he is at (4, 8).
- After walking south for 6 km, he is at (4, 2).
- After walking east for 3 km, he is at (7, 2).
Step 3: Calculate the distance from the starting point.
The distance between the starting point (0, 0) and the final position (7, 2) is given by the distance formula:
\[
\text{Distance} = \sqrt{(7 - 0)^2 + (2 - 0)^2} = \sqrt{49 + 4} = \sqrt{53} \approx 7.62 \text{ km}.
\]
Step 4: Conclusion.
Thus, the person is 7.62 km from the starting point, and the correct answer is (c).
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