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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Directions: Read the information given below carefully and answer the questions accordingly:
Rashmi stepped out of her college and walked 15 m towards South. She then took a left turn and walked 35 m to reach a pastry shop. She then took a right turn and walked 15 m. She then took a right turn and walked 35 m to reach her house. What is the approximate shortest distance between Rashmi's college and her house via the pastry shop?
Important Questions from Direction and Distance Turns
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
A boy starts from his home northward in order to go to a hotel. He took right turn and took left to reach the hotel. Which direction is the hotel facing?
Arun went 6 m from his home towards south and turned left to cover 8 m. Again he turned left and covered 6 m. He again turned right and covered 4 m. What was the direct distance from his home and which direction was he facing?
Sri walked 4 km towards east from home to school, and he turned three times right side of 6 km respectively. What is the distance between his home and the school?
