Understanding Direction and Distance Problems
This problem involves understanding directions and distances travelled. Vijendra starts from his home and makes a series of turns and walks specific distances, eventually returning home. To find the unknown distance X, we need to analyze his movements and see how they cancel out to bring him back to his starting point.
Breaking Down Vijendra's Walk
Let's list each step Vijendra takes:
- Starts at Home.
- Walks X metres towards the West.
- Turns left (now facing South) and walks 23 metres.
- Turns left again (now facing East) and walks 36 metres.
- Turns left again (now facing North) and walks 23 metres.
- Finally, turns left (now facing West) and walks 18 metres to reach his Home.
Analysing Net Displacement to Find Distance X
When someone returns to their starting point (like home in this case), their total displacement is zero. This means the total distance covered in one direction must be cancelled out by the total distance covered in the opposite direction.
Let's look at the movements in North-South and East-West directions:
- North-South Movements: Vijendra walks 23 metres South and then 23 metres North. These two movements are equal in magnitude and opposite in direction, so they cancel each other out (
23 metres South - 23 metres North = 0net North/South movement). - East-West Movements: Vijendra walks X metres West, then 36 metres East, and finally 18 metres West. For him to return home, the total distance covered towards the West must be equal to the total distance covered towards the East.
Total distance moved West = X metres + 18 metres = \(X + 18\) metres
Total distance moved East = 36 metres
Since he returns home, the total West distance must equal the total East distance:
\(X + 18 = 36\)
Calculating the Value of X
Now, we can solve the equation for X:
\(X = 36 - 18\)
\(X = 18\)
So, the value of X is 18 metres.
Summary of Movements
Let's summarise the movements with X = 18:
| Step | Direction | Distance (m) |
|---|---|---|
| 1 | West | 18 (X) |
| 2 | South | 23 |
| 3 | East | 36 |
| 4 | North | 23 |
| 5 | West | 18 |
Total West distance = 18 + 18 = 36 metres
Total East distance = 36 metres
Total South distance = 23 metres
Total North distance = 23 metres
Net East/West movement = 36 East - 36 West = 0
Net North/South movement = 23 North - 23 South = 0
Since both net movements are zero, Vijendra successfully returns to his starting point (home).
Final Answer for Distance X
The calculated value for X is 18.
Revision Table: Direction and Distance Concepts
| Concept | Explanation | Key for Problems |
|---|---|---|
| Starting Point | The initial position before any movement. | Reference for final position. |
| Direction | North, South, East, West, and intermediate directions. | Determines the line of movement. |
| Distance | Magnitude of movement along a path. | Used in calculations of displacement. |
| Turn Left/Right | Changes direction by 90 degrees clockwise (Right) or anti-clockwise (Left). | Crucial for tracing the path. |
| Displacement | The shortest distance between the starting and ending points. | Zero when returning to the starting point. |
Additional Information: Solving Return-to-Origin Problems
Problems where a person returns to their starting point are often solved by balancing the movements in opposite directions. Here's a general approach:
- Draw a simple diagram to visualise the path.
- List all movements and their directions.
- Group movements by opposing directions (North vs. South, East vs. West).
- If the person returns to the start, the total distance in one direction must equal the total distance in the opposite direction for each pair of opposing directions.
- Set up equations based on this principle and solve for any unknowns.
- Be careful with turns (left/right) as they change the subsequent direction of movement.
Similar Questions
Ramesh starts his journey by walking 2 kilometres towards the North. Then he takes a right turn and walks 1 kilometre. Again takes a right turn and walk 2 kilometers. Now which direction is he facing?
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To attend an exam, Sudhir reached the school by travelling 5 km towards South, and after a sharp left turn, he travelled for about 10 km. He again made a sharp left turn and reached in front of the school by travelling 5 km more. Which direction is Sudhir’s starting point from the school?
Aman starts from a point, walks 3 meters north, turns right and walks 3 meters, turns right again and walks 3 meters. Which direction is he facing now?
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Johnson left for his office in his car. He drove 15km towards North and then 10km towards West. He then turned to South and covered 5km. Further, he turned to East & moved 10km. How far & in which direction is he from his starting point?
From her house Rimi went 20 km to the north. Then she turned west and covered 15 km. Then she turned south and covered 10 km. Finally turning east, she covered 15 km. In which direction is she from her house?
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
