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.
Important Questions from Direction and Distance
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
Srinija walked 9 km towards the west from her home, then turned towards the south and walked 11 km. Then she walked 13 km towards the east, and finally walked 4 km towards the west. How far is Srinija from her initial position?
