Correct Option (2)
The woman's final position is determined by vector addition of her movements:
- Initial movement: 12 km North. Position: (0, 12).
- Second movement: 6 km South. Net Northward displacement: 12 - 6 = 6 km. Position: (0, 6).
- Third movement: 8 km East. Final position: (8, 6).
The net displacement from the starting point is 8 km East and 6 km North. This places her in a direction North of East.
The angle (θ) with respect to the East axis is given by:
tan(θ) = (Vertical displacement) / (Horizontal displacement) = 6/8 = 0.75.
Given tan(45°) = 1, and tan(θ) = 0.75, it follows that θ < 45°.
Thus, her position is at an angle less than 45° North of East from the starting point.
Incorrect Options:
- An angle less than 45° South of East: Incorrect, as the net vertical displacement is 6 km North, not South.
- An angle more than 45° South of East: Incorrect. The displacement is North, not South, and the calculated angle is less than 45°.
- An angle more than 45° North of East: Incorrect. While the direction is North of East, the calculated angle (θ) is less than 45° because tan(θ) = 0.75 < tan(45°).
