Mr. Yanki's Driving Problem: Finding the Return Path
This problem involves tracking movement based on directions and distances to find the shortest path back to the starting point. We can solve this by treating the movements as vectors or by using a coordinate system.
Understanding Mr. Yanki's Movements
Let's break down each step of Mr. Yanki's journey. We'll use a coordinate system where Point A is the origin (0, 0). We'll assume North corresponds to the positive y-axis and East corresponds to the positive x-axis. Therefore, South is the negative y-axis and West is the negative x-axis.
Tracking Position with Coordinates
We can track Mr. Yanki's position after each segment of his journey. A table helps visualize these changes.
| Movement Segment | Direction Driven | Distance (km) | Turn Made | Facing Direction | Coordinate Change (Δx, Δy) | Current Position (x, y) |
|---|---|---|---|---|---|---|
| Start (Point A) | - | - | - | - | (0, 0) | (0, 0) |
| 1 | South | 17 | - | South | (0, -17) | (0, -17) |
| 2 | West | 19 | Right | West | (-19, 0) | (-19, -17) |
| 3 | North | 29 | Right | North | (0, 29) | (-19, 12) |
| 4 | East | 15 | Right | East | (15, 0) | (-4, 12) |
| 5 | South | 1 | Right | South | (0, -1) | (-4, 11) |
| 6 | East | 6 | Left | East | (6, 0) | (2, 11) |
| 7 (Stop at P) | South | 11 | Right | South | (0, -11) | (2, 0) |
Calculating Final Position
After all the movements, Mr. Yanki stops at Point P. Let's calculate the net displacement in the x (East-West) and y (North-South) directions:
- Net East-West Displacement: Sum of x-changes = $0 + (-19) + 0 + 15 + 0 + 6 + 0 = 2$ km. This means Point P is 2 km East of Point A.
- Net North-South Displacement: Sum of y-changes = $(-17) + 0 + 29 + 0 + (-1) + 0 + (-11) = 17 - 17 = 0$ km. This means Point P is on the same East-West line as Point A.
So, the final position of Point P relative to Point A is (2, 0).
Determining Return Path to Point A
Mr. Yanki is currently at Point P (2, 0) and needs to return to Point A (0, 0).
The required displacement vector from P to A is:
Displacement = (Target x - Current x, Target y - Current y)
Displacement = ($0 - 2$, $0 - 0$) = (-2, 0)
A coordinate change of (-2, 0) means moving 2 units in the negative x-direction.
- The negative x-direction corresponds to the West direction.
- The magnitude of the movement is $ \sqrt{(-2)^2 + (0)^2} = \sqrt{4} = 2 $ km.
Therefore, Mr. Yanki needs to drive 2 km towards the West to reach Point A again.
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?
