Question

Gyan Prakash left for his college in his car -
(J) He drove 15 km towards the North and then 10 km towards the West.
(K) He then turned South and covered 5 km.
(L) Further, he turned to the East and moved 8 km.
(M) Finally, he turned right and drove 10 km.
How far and in which direction is he from his starting point?

• A. 2 km West
• B. 5 km East
• C. 3 km North
• D. 6 km South

Hint:

Always draw a quick direction compass (N, S, E, W) on your rough sheet. Draw each movement vector proportionally to scale so you can visually verify your mathematical coordinates.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to track the movement of Gyan Prakash along different directions (North, South, East, West) and calculate his final distance and direction relative to his starting point.

Step 2: Key Formula or Approach:
We can use a 2D Cartesian coordinate system to track the positions:
- Let the starting point be the origin \( (0, 0) \).
- North represents \( +y \) direction, South represents \( -y \) direction.
- East represents \( +x \) direction, West represents \( -x \) direction.

Step 3: Detailed Explanation:
Let's calculate his coordinates after each step:
1. Initial Position: \( (0, 0) \)
2. Step (J): He drove 15 km North, then 10 km West.
- Going 15 km North: \( (0, 15) \)
- Going 10 km West: \( (-10, 15) \)
3. Step (K): He turned South and covered 5 km.
- Going 5 km South: \( (-10, 15 - 5) = (-10, 10) \)
4. Step (L): He turned East and moved 8 km.
- Going 8 km East: \( (-10 + 8, 10) = (-2, 10) \)
5. Step (M): Finally, he turned right and drove 10 km.
- Since he was moving East, turning right means turning towards the South.
- Going 10 km South: \( (-2, 10 - 10) = (-2, 0) \)
At the end of his journey, his coordinates are \( (-2, 0) \).
Comparing \( (-2, 0) \) with the starting point \( (0, 0) \):
- The distance is \( 2 \, \text{km} \).
- The direction is along the negative x-axis, which is West.
Therefore, he is 2 km West from his starting point.

Step 4: Final Answer:
(A) 2 km West