From his home, Mohan started his walk towards the east and walked 90 metres before turning towards his right. He then walked 20 metres, turned right again and walked further 30 metres. From there, he turned towards the north and walked further 100 metres to end his walk. In which direction is his home from this position?
South-west
Mohan's Walking Path Analysis
This solution details Mohan's walk step-by-step to find the direction of his home from his final location.
Understanding Cardinal Directions and Turns
The walk involves movements along cardinal directions (East, North) and turns. A 'turn right' means changing direction 90 degrees clockwise.
Tracing Mohan's Movements
Let's break down Mohan's journey from his home:
- Start: At home.
- Move 1: Walks 90 metres East. His position is now 90m East of home.
- Turn 1: Turns right. Facing East, a right turn means he now faces South.
- Move 2: Walks 20 metres South. His position is now 90m East and 20m South of home.
- Turn 2: Turns right again. Facing South, a right turn means he now faces West.
- Move 3: Walks 30 metres West. His net East-West position changes. His position is now (90m East - 30m West) = 60m East, and still 20m South of home.
- Turn 3: Turns towards the North.
- Move 4: Walks 100 metres North. His net North-South position changes. His position is now 60m East, and (20m South + 100m North) = 80m North of home.
Table Summarizing Displacements
| Movement Segment | Direction | Distance (metres) | East-West Change | North-South Change |
|---|---|---|---|---|
| 1 | East | 90 | +90 m | 0 m |
| 2 | South | 20 | 0 m | -20 m |
| 3 | West | 30 | -30 m | 0 m |
| 4 | North | 100 | 0 m | +100 m |
Calculating Final Position Relative to Home
We sum the changes along each axis:
- Total East-West Displacement: (+90 m) + (-30 m) = +60 m. This means Mohan's final position is 60 metres East of his starting point (home).
- Total North-South Displacement: (-20 m) + (+100 m) = +80 m. This means Mohan's final position is 80 metres North of his starting point (home).
So, Mohan's end position is 60 metres East and 80 metres North relative to his home.
Finding Home's Direction from Mohan's Final Position
The question asks for the direction of his home FROM his final position. We found his final position is 60m East and 80m North of home. To find home's direction from the final point, we reverse these directions:
- The opposite direction of 60m East is 60m West.
- The opposite direction of 80m North is 80m South.
Therefore, home is located 60 metres West and 80 metres South from Mohan's final position. This combined direction is South-West.
Similar Questions
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Important Questions from Direction and Distance Turns
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