A man drives 20 km towards the East and turns to the right-hand side and takes a drive of another 3 km. He then drives towards the West (turning to his right) another 3 km. He then turns to his left and walks another 2 km. Afterward, he turns to his right and travels 17 km. How far is he from his starting point?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5 km
To find the distance from the starting point, let's track the man's movement step-by-step on a coordinate plane, starting at $(0, 0)$.
Step-by-Step Path Tracking
- Starts at (0, 0).
- 20 km East: He moves to $(20, 0)$.
- Turns right (South) and drives 3 km: He is now at $(20, -3)$.
- Turns right (West) and drives 3 km: He is now at $(17, -3)$.
- Turns left (South) and walks 2 km: He is now at $(17, -5)$.
- Turns right (West) and travels 17 km: * His current x-coordinate is $17$. Moving $17\text{ km}$ West means $17 - 17 = 0$.
- He is now at $(0, -5)$.
Calculating the Final Distance
- Starting Point: $(0, 0)$
- Ending Point: $(0, -5)$
The distance between $(0, 0)$ and $(0, -5)$ is simply the vertical difference:
$\text{Distance} = \sqrt{(0-0)^2 + (0 - (-5))^2} = \sqrt{0^2 + 5^2} = \mathbf{5\text{ km}}$
The man is exactly $5\text{ km}$ South of his starting point.