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
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
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?
