Pinky walks a distance 600m towards east, turns left moves 500m, then again turns left and walks 600m and then turns left again and moves 500m and halts. At what distance (in meters) is she from the starting point?
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Understanding Distance and Displacement
This problem involves analyzing movement in different directions. We need to find the final distance from the starting point after a series of movements and turns. Let's trace Pinky's path step by step.
Tracing Pinky's Movement Path
Pinky starts at a certain point. Let's call this the starting point (S).
- First, she walks 600m towards the east. Let's say she reaches point A.
- Then, she turns left. When facing east, a left turn means turning towards the north. She moves 500m in this direction. Let's say she reaches point B.
- Next, she again turns left. From point B, she is facing north. A left turn from north is towards the west. She walks 600m in this direction. Let's say she reaches point C.
- Finally, she turns left again. From point C, she is facing west. A left turn from west is towards the south. She moves 500m in this direction. Let's say she reaches point D and halts there.
Analysing the Directions and Distances
Let's look at the movements along the East-West axis and the North-South axis separately.
- East-West Movement: She moves 600m East, and then 600m West. These two movements are in opposite directions and cover the same distance.
- North-South Movement: She moves 500m North, and then 500m South. These two movements are also in opposite directions and cover the same distance.
Imagine setting up a coordinate system with the starting point at (0,0). East is the positive x-direction, North is the positive y-direction, West is the negative x-direction, and South is the negative y-direction.
| Step | Direction | Distance (m) | Change in Position (x, y) | Current Position (relative to Start) |
|---|---|---|---|---|
| Start | - | 0 | (0, 0) | (0, 0) |
| 1 | East | 600 | (+600, 0) | (+600, 0) |
| 2 (Left turn) | North | 500 | (0, +500) | (+600, +500) |
| 3 (Left turn) | West | 600 | (-600, 0) | (+600 - 600, +500) = (0, +500) |
| 4 (Left turn) | South | 500 | (0, -500) | (0, +500 - 500) = (0, 0) |
After the four steps, Pinky's final position is (0,0) relative to the starting point, which was also at (0,0).
Calculating the Distance from Starting Point
The distance from the starting point is the straight-line distance between the starting position and the final position. The starting position is (0,0) and the final position is (0,0).
The distance (d) between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a 2D plane is given by the distance formula:
\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
In this case, $(x_1, y_1) = (0,0)$ and $(x_2, y_2) = (0,0)$.
\(d = \sqrt{(0 - 0)^2 + (0 - 0)^2}\)
\(d = \sqrt{0^2 + 0^2}\)
\(d = \sqrt{0 + 0}\)
\(d = \sqrt{0}\)
\(d = 0\)
The distance from the starting point is 0 meters.
Conclusion on Distance from Starting Point
The movements effectively cancelled each other out, bringing Pinky back to her original starting location. The total distance travelled is \(600m + 500m + 600m + 500m = 2200m\), but the distance from the starting point (displacement) is 0m.
Revision Table: Key Concepts
| Concept | Explanation | How it applies here |
|---|---|---|
| Distance Traveled | The total length of the path covered during movement. | Total distance = 600m + 500m + 600m + 500m = 2200m. |
| Displacement | The straight-line distance and direction from the starting point to the ending point. It's a vector quantity. | The ending point is the same as the starting point, so displacement is 0m. |
| Left Turn (in Directions) | From East, Left is North. From North, Left is West. From West, Left is South. From South, Left is East. | Used to determine the direction of movement after each turn. |
Additional Information: Directional Problems
Solving directional problems often involves visualizing the path or using coordinates. Key things to remember:
- Movements in opposite directions cancel each other out if the distances are equal (e.g., 600m East and 600m West).
- If movements are perpendicular (e.g., North and East), you might use the Pythagorean theorem to find the straight-line distance (displacement) from a point.
- 'Distance from the starting point' usually refers to the magnitude of the displacement.
- Drawing a simple diagram can be very helpful in visualizing the path and understanding the net effect of the movements.
- Left and right turns depend on the current facing direction.
Important Questions from Direction Sense Test
A man moves to the east side, then turns left, then right, and then further turns right again and then moves left. Now, in which direction is the man?
Sunita rode her scooty Northward, then turned left and then again rode to her left 4 km. She found herself exactly 2 km. West to her starting point. How far did she ride Northwards initially?
One evening before sunset, two friends Shahrukh and Rakesh were talking to each other face-to-face. If Rakesh’s shadow is exactly to his right side, which direction was Shahrukh facing?
A girl is facing north. She turns 90° in the anti-clockwise direction and then 45° in the clockwise direction. Which direction is she facing now?
A boy runs 4 km to East side, then turns right and runs 6 km, and then turns left and runs 8 km. Again turns left to run 3 km, again turns right 4 km, then turns right 1 km. Now the boy is in which direction?
