Solving Rohan's Directional Walk Problem
This problem involves tracking a person's movement through different directions and calculating their final distance from the starting point. Let's break down Rohan's journey step by step.
Tracking Rohan's Path
We can visualize Rohan's path or use coordinates to find his final position relative to his start.
- Step 1: Northward Movement
Rohan starts at a point (let's call it the origin) and walks 3 kms towards North. His position is now 3 kms North of the start.
- Step 2: First Left Turn (Westward)
He turns to his left. Since he was facing North, his left is West. He walks 2 kms West. His position is now 3 kms North and 2 kms West of the start.
- Step 3: Second Left Turn (Southward)
He again turns left. Now facing West, his left is South. He walks 3 kms South. This movement cancels out his initial 3 kms Northward movement. He is now on the same horizontal line as his starting point, but 2 kms West of it.
- Step 4: Third Left Turn (Eastward)
He turns left again. Facing South, his left is East. He walks for 3 kms. Starting from 2 kms West of the origin, walking 3 kms East means he first covers the 2 kms back to the starting point's North-South line, and then continues another 1 km East.
Calculating Final Distance from Start
After the final step, Rohan is 1 km East of the North-South line passing through his starting point. Since his North-South displacement is zero (3 km North - 3 km South = 0 km), his final position is exactly 1 km East of his starting point.
Therefore, the distance from the starting point is simply this eastward displacement.
Final Distance = 1 km
Using Coordinates (Alternative Method)
Let the starting point be (0, 0).
- After walking 3 km North: Position is (0, 3).
- Turning left (West) and walking 2 km: Position is (-2, 3).
- Turning left (South) and walking 3 km: Position is (-2, 3 - 3) = (-2, 0).
- Turning left (East) and walking 3 km: Position is (-2 + 3, 0) = (1, 0).
The starting point is (0, 0) and the final point is (1, 0).
The distance using the distance formula:
Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Distance = $\sqrt{(1 - 0)^2 + (0 - 0)^2}$
Distance = $\sqrt{1^2 + 0^2}$
Distance = $\sqrt{1}$
Distance = $1$ km.
Both methods confirm that Rohan is 1 km away from his 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?
