Sunny drives 3 km towards west from point A. He then takes a right turn and drives 6 km. Again, he takes a right turn and drives 3 km. Finally, he takes a left turn and drives 3 km to reach point B. How far and towards which direction should he drive now in order to reach point A again?
9 km towards south
Analyzing Sunny's Journey
Let's carefully trace Sunny's path from point A to point B. We need to determine his final position relative to point A to figure out how to return.
Step-by-Step Path Analysis
We can break down Sunny's journey into several segments:
- Starting Point: Point A.
- Segment 1: Drives 3 km towards west from point A. Let's call the end of this segment Point C. Relative position: 3 km West of A.
- Segment 2: From Point C, he takes a right turn. A right turn from West is North. He drives 6 km towards north. Let's call the end of this segment Point D. Relative position: 3 km West and 6 km North of A.
- Segment 3: From Point D, he again takes a right turn. A right turn from North is East. He drives 3 km towards east. Let's call the end of this segment Point E. Relative position: From Point D (3W, 6N), moving 3 km East cancels out the 3 km West displacement. So, Point E is 0 km West/East and 6 km North of A. Point E is 6 km North of A.
- Segment 4: From Point E, he takes a left turn. A left turn from East is North. He drives 3 km towards north to reach point B. Relative position: From Point E (6N), moving 3 km North adds to the North displacement. So, Point B is (6 km North + 3 km North) = 9 km North of A.
So, Point B is located 9 km directly North of Point A.
Calculating the Return Journey to Point A
Sunny is currently at Point B, which is 9 km North of Point A. To return to Point A, he needs to travel directly from Point B back to Point A.
Since Point B is 9 km North of A, to get back to A, Sunny must drive 9 km in the opposite direction of North, which is South.
Therefore, he should drive 9 km towards south to reach point A again.
| Segment | Direction | Distance (km) | Displacement | Position relative to A |
|---|---|---|---|---|
| Start | - | 0 | - | Point A |
| 1 | West | 3 | 3 km West | 3 km West of A |
| 2 | North | 6 | 6 km North | 3 km West, 6 km North of A |
| 3 | East | 3 | 3 km East | 6 km North of A |
| 4 | North | 3 | 3 km North | 9 km North of A (Point B) |
Revision Table: Directions and Turns
| Facing Direction | Right Turn Leads To | Left Turn Leads To |
|---|---|---|
| North | East | West |
| South | West | East |
| East | South | North |
| West | North | South |
Additional Information: Displacement in Direction Problems
In direction and distance problems, it's important to understand the difference between total distance traveled and displacement.
- Total Distance: This is the sum of the lengths of all segments traveled (3 km + 6 km + 3 km + 3 km = 15 km in this case). This is the actual length of the path taken.
- Displacement: This is the shortest straight-line distance from the starting point to the ending point, along with the direction. It's a vector quantity. In this problem, Sunny's total displacement is 9 km North from Point A to Point B.
To return to the starting point (Point A), Sunny needs to cover a distance equal to the magnitude of the displacement (9 km) in the opposite direction (South).
Similar Questions
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Important Questions from Direction and Distance Turns
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A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
