Swapnil goes to the park every day for walking. One morning, he started walking from his home and walked 40 km towards North. Then, he turned to the right and walked 60 km. Again, he turned right and walked 40 km. Lastly, he took a left turn and walked 30 km. In which direction is he now from his home?
East
Understanding Direction Problems: Swapnil's Walk
This question asks for Swapnil's final direction from his starting point (home) after a series of movements and turns. To solve this, we can trace Swapnil's path step by step, considering the distances and turns.
Step-by-Step Analysis of Swapnil's Movement
Let's break down Swapnil's journey from his home:
- Starts from Home: Swapnil begins at his home. We can consider this the origin point, like (0,0) on a coordinate system.
- Walks 40 km towards North: From home, he moves 40 km directly North. His position is now 40 km North of home. If home is (0,0), this is like moving to (0, 40).
- Turns Right and Walks 60 km: From his current position (40 km North), he turns right. When facing North, a right turn is towards the East. He walks 60 km East. His position is now 60 km East and 40 km North of home. This is like moving to (0 + 60, 40) = (60, 40).
- Turns Right Again and Walks 40 km: From his current position (60 km East, 40 km North), he turns right. When facing East, a right turn is towards the South. He walks 40 km South. His position is now 60 km East and (40 - 40) km North of home. This is like moving to (60, 40 - 40) = (60, 0).
- Takes a Left Turn and Walks 30 km: From his current position (60 km East, 0 km North/South relative to the original North-South line), he turns left. When facing South, a left turn is towards the East. He walks 30 km East. His position is now (60 + 30) km East and 0 km North/South of home. This is like moving to (60 + 30, 0) = (90, 0).
Summarizing Swapnil's Path and Position
We can summarize Swapnil's movement and position relative to his home (the starting point) in a table:
| Step | Movement | Direction | Distance | Position Relative to Home (Conceptual) |
|---|---|---|---|---|
| Start | At Home | - | 0 km | (0,0) |
| 1 | Walks | North | 40 km | (0, 40) |
| 2 | Turns Right, Walks | East | 60 km | (60, 40) |
| 3 | Turns Right, Walks | South | 40 km | (60, 0) |
| 4 | Turns Left, Walks | East | 30 km | (90, 0) |
Determining Final Direction from Home
Swapnil's final position is conceptually at (90, 0). His starting point (home) is at (0,0). To find the direction from home, we look at his final position relative to the origin.
- He is 90 km towards the East from home (positive x-axis direction).
- He is 0 km North or South from the East-West line passing through home (y-coordinate is 0).
Since his final position is purely in the East direction from his starting point, he is now in the East direction from his home.
Final Answer Confirmation
Based on the step-by-step tracing of Swapnil's path, his final location is directly East of his starting point (home). The total displacement North-South cancels out (40 km North, then 40 km South), leaving only an Eastward displacement (60 km East, then 30 km East, totalling 90 km East).
Revision Table: Key Concepts in Direction Problems
| Concept | Explanation | How it applies here |
|---|---|---|
| Directions | North, South, East, West are the four main directions. | Swapnil walks in these directions. |
| Turns | Turning right or left changes your facing direction. Right turn is +90° clockwise, Left turn is -90° clockwise (or +90° counter-clockwise). | Turning right from North is East, right from East is South, left from South is East. |
| Starting Point | The reference point from where the movement begins. | Swapnil's home is the starting point. Final direction is asked relative to this. |
| Final Position | The location where the movement ends. | The final location after all movements. |
| Direction From Start | The compass direction from the starting point to the final position. | This is what the question asks for. |
Additional Information: Visualizing Movement
Visualizing the path is very helpful in direction and distance problems. You can sketch a diagram with arrows representing each leg of the journey. Alternatively, using a coordinate system where North is the positive y-axis, South is the negative y-axis, East is the positive x-axis, and West is the negative x-axis can precisely track position.
- Starting at (0,0).
- North 40 km: (0, 40).
- Right turn (East) 60 km: (0+60, 40) = (60, 40).
- Right turn (South) 40 km: (60, 40-40) = (60, 0).
- Left turn (East) 30 km: (60+30, 0) = (90, 0).
The final coordinates (90, 0) clearly show a position 90 units in the positive x direction (East) and 0 units in the y direction (North/South) relative to the origin (0,0), confirming the direction from home is East.
Similar Questions
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
Tamanna is walking towards the north from her house. After 500 metres she turns left and walks for 500 metres. Then she turns left and walks 250 metres to reach her friend’s house. In Which direction is her house from her friend’s house?
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Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
