Question

A person moves 15 km East direction, then turns towards North and moves 4 km. From here he turns towards West and travels 12 km. How far and in which direction is he from the starting point?

• A. 31 km, South-West
• B. 5 km, North-East
• C. 19 km, North-East
• D. 27 km, South-West

Hint:

To solve direction and distance problems, always break down movements along North-South and East-West axes and then use the Pythagoras theorem for resultant distance.

Answer 1

The Correct Option is B

Let's analyze the movement step by step:
1. The person first moves 15 km towards the East.
2. Then, the person turns North and moves 4 km.
3. From this point, the person turns West and moves 12 km.
Now, calculate the net displacement from the starting point:
- East-West displacement:
Moved 15 km East initially, then 12 km West.
Net East displacement = 15 km - 12 km = 3 km East.
- North-South displacement:
Moved 4 km North.
Net North displacement = 4 km North.
To find the straight-line distance from the starting point, use Pythagoras theorem:
Distance = \(\sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{km}\)
The direction from the starting point is North-East because the net movement is 3 km East and 4 km North.
Hence, the person is 5 km away in the North-East direction.
Therefore, the correct answer is option (B) 5 km, North-East.