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
Two different positions of the same dice with faces K, B, V, M, P, and T are shown below. Select the letter that will be on the face opposite to the one having B.
Select the number from among the given options that can replace the question mark (?) in the following series.
3, 6, 9, 18, 21, ?
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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?
