Solving Aditi's Movement Puzzle
This solution explains how to determine the direction and distance of Aditi's home from her final location after a series of movements. We will use a coordinate system to track her path accurately.
Setting Up the Coordinate System
To visualize Aditi's journey, we can use a standard Cartesian coordinate system:
- Let Aditi's home be the origin (0, 0).
- The positive y-axis represents North.
- The negative y-axis represents South.
- The positive x-axis represents East.
- The negative x-axis represents West.
Tracking Aditi's Movements Step-by-Step
We will break down each part of Aditi's walk and note her position and direction:
| Step | Movement Description | Direction Change | Distance Moved | Position Change (Δx, Δy) | Current Position (x, y) | Current Facing Direction |
|---|---|---|---|---|---|---|
| 1 | Starts from home, walks South | N/A | 18 m | (0, -18) | (0, -18) | South |
| 2 | Turns right, walks | From South, right is West | 12 m | (-12, 0) | (0 - 12, -18) = (-12, -18) | West |
| 3 | Takes a left turn, walks | From West, left is South | 6 m | (0, -6) | (-12, -18 - 6) = (-12, -24) | South |
| 4 | Walks North | N/A | 24 m | (0, +24) | (-12, -24 + 24) = (-12, 0) | North |
| 5 | Turns left, walks | From North, left is West | 12 m | (-12, 0) | (-12 - 12, 0) = (-24, 0) | West |
Calculating Aditi's Final Position
After completing all five steps, Aditi's final position is (-24, 0).
This means her final location is 24 meters West of her starting point (home).
Finding Home's Location Relative to Final Position
The question asks for the direction and distance of her home from her final position.
- Aditi's Home Position (\(P_{home}\)) = (0, 0)
- Aditi's Final Position (\(P_{final}\)) = (-24, 0)
To find the location of home relative to the final position, we calculate the displacement vector from the final position to the home position:
Displacement Vector \(\vec{d} = P_{home} - P_{final}\)
We use LaTeX for the calculation:
\(\vec{d} = (0, 0) - (-24, 0)\)
Subtracting the coordinates:
\(\vec{d} = (0 - (-24), 0 - 0)\)
\(\vec{d} = (24, 0)\)
Interpreting the Result
The resulting displacement vector is \(\vec{d} = (24, 0)\).
- The x-component is \(+24\). This signifies a movement of 24 meters towards the East (positive x-direction).
- The y-component is \(0\). This signifies no movement needed in the North-South direction.
The distance is the magnitude of this vector:
Distance \(= \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(24)^2 + (0)^2} = \sqrt{576} = 24\) meters.
Therefore, Aditi's home is located 24 meters East from her final position.
Similar Questions
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Rahman went from his office to the district headquarters. He started his journey facing west. First, he went 20 km straight; then he turned to his left and went 9 km; finally, he turned right and went 20 km to reach the district headquarters.
What is the shortest distance between Rahman’s office and the district headquarters?In a morning after sunrise, a boy rode his bicycle 4 km towards west. Then the took right turn and rode 6 km then he right turn and rode 6 km to reach is school. In which direction the school is from then starting point?
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?
