Charanjit walked South West 30 metres. Then after he turned left and cover 60 metres. Now he is in which direction form is original position?

1. Break Down the Problem

• Identify the initial direction: Charanjit walked Southwest (SW).
• Determine the next direction after the turn: After turning left from SW, he will face Southeast (SE).
• Calculate the total distance covered.

2. Relevant Concepts

• We will use a coordinate system to analyze the movements.
• Define directions as follows:
  • North (N) = 0 degrees
  • East (E) = 90 degrees
  • South (S) = 180 degrees
  • West (W) = 270 degrees
  • Southwest (SW) = 225 degrees
  • Southeast (SE) = 135 degrees

3. Analysis and Detail

1. First Movement:

   • From the original position, walking SW (225 degrees) for 30 metres can be represented as: $x = 30 \cdot \cos(225^\circ) = 30 \cdot \left(-\frac{1}{\sqrt{2}}\right) \approx -21.21$ $y = 30 \cdot \sin(225^\circ) = 30 \cdot \left(-\frac{1}{\sqrt{2}}\right) \approx -21.21$
   • New coordinates after the first movement: (-21.21, -21.21).

2. Second Movement:

   • Turning left means facing SE (135 degrees). Walking 60 metres: $x_{\text{new}} = -21.21 + 60 \cdot \cos(135^\circ) = -21.21 + 60 \cdot \left(-\frac{1}{\sqrt{2}}\right) \approx -21.21 - 42.43 = -63.64$ $y_{\text{new}} = -21.21 + 60 \cdot \sin(135^\circ) = -21.21 + 60 \cdot \left(\frac{1}{\sqrt{2}}\right) \approx -21.21 + 42.43 = 21.21$
   • New coordinates after the second movement: (-63.64, 21.21).

4. Verify and Summarize

• To find the direction from the original position (0, 0) to the new position (-63.64, 21.21), we analyze the coordinates.
• Since the x-coordinate is negative and y-coordinate is positive, Charanjit is in the Northwest direction from the original position.

Final Answer

Charanjit is in the Northwest direction from his original position.