Question

Sapna travels 10 km North, turns left 4 km, turns right 5 km, then turns right 4 km. How far is she from the starting point and in which direction?

• A. 15 km South
• B. 10 km North
• C. 15 km East
• D. 15 km North
• E. 10 km East

Hint:

Opposite directions (East vs West, North vs South) can be treated as positive and negative values to quickly find the net displacement.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Track the displacement on a coordinate plane, summing up the vertical (North/South) and horizontal (East/West) movements.
Step 2: Identifying the Vector of Change:
- Move 1: 10 km North. - Move 2: 4 km West (Left turn from North). - Move 3: 5 km North (Right turn from West). - Move 4: 4 km East (Right turn from North).
Step 3: Calculation:
- Horizontal (East-West): She moved 4 km West, then 4 km East. These cancel out ($4 - 4 = 0$), so she is back on the same vertical line as the start. - Vertical (North-South): She moved 10 km North and then another 5 km North. Total = $10 + 5 = 15$ km North.
Step 4: Final Answer:
Sapna is 15 km North from the starting point. Thus, the correct option is (d).