Step-by-Step Solution: Girl's Walk from School
This problem requires us to determine the final position of a girl relative to her starting point (the school gate) after a series of movements. We can track her position using a coordinate system, where the school gate is the origin $(0, 0)$. We'll define East as the positive x-direction, West as the negative x-direction, North as the positive y-direction, and South as the negative y-direction.
Tracking the Girl's Movements
Let's follow each step of her journey:
- Starting Point: School Gate at coordinates $(0, 0)$.
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1. Walks 10 m East:
- Movement: $+10$ m along the x-axis.
- New Position: $(0 + 10, 0) = (10, 0)$.
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2. Walks 4 m South:
- Movement: $-4$ m along the y-axis.
- New Position: $(10, 0 - 4) = (10, -4)$.
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3. Walks 8 m West:
- Movement: $-8$ m along the x-axis.
- New Position: $(10 - 8, -4) = (2, -4)$.
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4. Walks 2 m North:
- Movement: $+2$ m along the y-axis.
- New Position: $(2, -4 + 2) = (2, -2)$.
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5. Turns right and walks 6 m:
- At this point, she is facing North (from the previous step). Turning right means she now faces East.
- Movement: $+6$ m along the x-axis.
- New Position: $(2 + 6, -2) = (8, -2)$.
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6. Turns left and walks 2 m:
- She is currently facing East. Turning left means she now faces North.
- Movement: $+2$ m along the y-axis.
- New Position: $(8, -2 + 2) = (8, 0)$.
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7. Turns left again and walks 6 m:
- She is currently facing North. Turning left means she now faces West.
- Movement: $-6$ m along the x-axis.
- Final Position: $(8 - 6, 0) = (2, 0)$.
Calculating Net Displacement
Alternatively, we can sum the displacements along each axis:
- East-West (x-axis) Displacement:
- Movements: $+10$ m (East), $-8$ m (West), $+6$ m (East), $-6$ m (West).
- Net x-displacement = $10 - 8 + 6 - 6 = 2$ m.
- North-South (y-axis) Displacement:
- Movements: $-4$ m (South), $+2$ m (North), $+2$ m (North).
- Net y-displacement = $-4 + 2 + 2 = 0$ m.
The net displacement is $2$ m in the East direction and $0$ m in the North-South direction. The final coordinates are $(2, 0)$.
Final Position Relative to School Gate
The final position $(2, 0)$ means the girl is 2 meters from the origin along the positive x-axis. Since the positive x-axis represents East, she is 2 meters East of the school gate.
Therefore, the girl is located 2 m East from the school gate.
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Important Questions from Direction and Distance
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Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
