A postman starts from the post office and cycles 13 km south, then turns west and cycles 10 km, then turns north and cycles 8 km, then turns east and cycles 2 km and then turns to his left and cycles 5 km. Where is he now with reference to his starting position?
8 km west
Understanding Direction and Distance Problems
This problem involves tracking a series of movements in different directions to find the final position relative to the starting point. We can solve this by breaking down the movements into components along the North-South axis and the East-West axis.
Step-by-Step Movement Analysis
Let's track the postman's journey from the starting point, the post office.
- Starting Point: Post Office (Let's consider this the origin (0,0)).
- First Movement: Cycles 13 km south. This movement is purely along the South axis.
- Second Movement: Turns west and cycles 10 km. This movement is purely along the West axis.
- Third Movement: Turns north and cycles 8 km. This movement is purely along the North axis.
- Fourth Movement: Turns east and cycles 2 km. This movement is purely along the East axis.
- Fifth Movement: Turns to his left and cycles 5 km. After moving east, a left turn means turning towards North. So, this movement is 5 km north.
Calculating Net Displacement
Now, let's sum up the total distance traveled in each cardinal direction:
- Total South movement: 13 km
- Total North movement: 8 km + 5 km = 13 km
- Total West movement: 10 km
- Total East movement: 2 km
Next, we calculate the net displacement along the North-South axis and the East-West axis.
Net Displacement along North-South Axis:
Net North displacement = Total North - Total South
Net North displacement = 13 km - 13 km = 0 km
This means the postman is at the same latitude (North-South position) as his starting point.
Net Displacement along East-West Axis:
Net West displacement = Total West - Total East
Net West displacement = 10 km - 2 km = 8 km
Since the Net West displacement is positive (meaning West movement was greater than East movement), the postman is to the west of his starting point.
Final Position Relative to Starting Point
Combining the net displacements:
- Net North/South displacement: 0 km
- Net East/West displacement: 8 km West
Therefore, the postman is 8 km west of his starting position at the post office.
We can summarize the movements in a table:
| Movement | Direction | Distance (km) | North (+)/South (-) | East (+)/West (-) |
|---|---|---|---|---|
| Start | - | 0 | 0 | 0 |
| 1 | South | 13 | -13 | 0 |
| 2 | West | 10 | 0 | -10 |
| 3 | North | 8 | +8 | 0 |
| 4 | East | 2 | 0 | +2 |
| 5 (Left after East) | North | 5 | +5 | 0 |
| Total Net | - | - | (-13 + 8 + 5) = 0 | (-10 + 2) = -8 |
A net displacement of -8 in the East/West column corresponds to 8 km West. A net displacement of 0 in the North/South column means no change in the North-South position.
Conclusion
Based on the calculations, the postman's final position is 8 km to the west of the post office.
Revision Table: Direction and Distance Concepts
| Concept | Explanation | How it applies here |
|---|---|---|
| Starting Point | Reference point for calculating final position. | The Post Office. |
| Direction | Path of movement (North, South, East, West, Left, Right). | Movements are broken down into cardinal directions. 'Left' after East is North. |
| Distance | Magnitude of movement in a specific direction. | Summed up for each cardinal direction. |
| Displacement | Straight-line distance and direction from start to end point. Calculated as net change in North-South and East-West. | Net change in N/S and E/W is calculated to find final displacement. |
Additional Information on Relative Position
When solving these types of direction and distance problems, it's helpful to think of movements as changes in coordinates on a grid, where North is positive Y, South is negative Y, East is positive X, and West is negative X. Starting at (0,0):
- 13 km South: (0, -13)
- Then 10 km West: (0 - 10, -13) = (-10, -13)
- Then 8 km North: (-10, -13 + 8) = (-10, -5)
- Then 2 km East: (-10 + 2, -5) = (-8, -5)
- Then 5 km Left (North): (-8, -5 + 5) = (-8, 0)
The final position is at coordinate (-8, 0). Relative to the start (0,0), this means 8 units in the negative X direction (West) and 0 units in the Y direction (North/South). This confirms the result: 8 km West of the starting position.
Similar Questions
Namia is facing the west. She turns left and walks 15 m. She turns left and walks 25 m. She again turns left and walks 40 m. She finally turns left and walks 40 m to reach home. In which direction is her home with respect to the starting point?
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(All turns are 90-degree turns only unless specified.)- Aryan starts from point P and walks for 4 m towards the south. Then he takes a left turn and walks for 3 m. Then he takes one more left turn and walks for 8 m. Then he takes a right turn and walks for 2 m. Then he takes the last right turn and walks for 4 m before stopping at point Q. Towards which direction should he walk in order to reach point P again? (All turns are 90-degree turns only unless specified.)
- Swara starts from point P and walks for 8 m towards the north. Then she takes a right turn and walks for 5 m. Then, again, she takes a right turn and walks for 4 m. One more time she takes a right turn and walks for 10 m. Then she takes a left turn and walks for 4 m before stopping at point Q. Towards which direction should she walk in order to reach Point P again? (All turns are 90-degree turns only unless specified.)
- Amita walks towards north for 5 m from point A. Then she takes a right turn and walks for 8 m. Then, again, she takes a right turn and walks for 3 m. Once again, she takes a right turn and walks for 2 m. Then she takes a left turn and walk for 2 m and stops at point B. Towards which direction should she walk in order to reach point A again? (All turns are 90-degree turns only unless specified.)
In the morning X and Y are walking towards each other in a park. When they meet each other, Y’s shadow falls straight in front of X. In which direction was X facing?
Mr. X starts from point ‘A’ travels 80 km towards west, takes a left turn, travels 50 km and reaches point ‘B’. What is the shortest distance between points ‘A’ and ‘B’?
Samarth heading towards north walked 10 m, he turns right and walks for 4 metres and then he turns left and walks 6 m. In which direction he is walking at last?
Samarth walks 10 kms towards east, then takes a right turn and walks 8 kms and again takes a left and walks 6 kms. In which direction is Samarth with respect to his starting position?
X walks 3 km towards west, and then turns and travels 4 km towards north. The shortest distance between the start and the end point of X’s journey is ______.
Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
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?
