Rakesh left home and walked $5$km southwards, then turned right and walked $2$km and again turned right and walked $5$ km and finally again turned left and walked $5$ km. The shortest distance between the final position and home is.
Understanding Rakesh's Directional Journey
Rakesh's movement can be broken down into distinct steps. We need to track his position relative to his starting point (home) to find the shortest distance.
- Step 1: Rakesh starts at home and walks 5 km South.
- Step 2: He turns right from the South direction (which means he faces West) and walks 2 km West.
- Step 3: He turns right again from the West direction (which means he faces North) and walks 5 km North.
- Step 4: He turns left from the North direction (which means he faces West) and walks 5 km West.
Calculating Net Displacement
To find the shortest distance, we calculate the net displacement in the North-South and East-West directions. Let's consider South and West as negative directions and North and East as positive directions for simplicity, or track them separately.
North-South Displacement:
- Movement South: $5$ km
- Movement North: $5$ km
- Net North-South Displacement = $5 \text{ km (South)} - 5 \text{ km (North)} = 0 \text{ km}$.
This means Rakesh ends up at the same North-South level as his home.
East-West Displacement:
- Movement West: $2$ km
- Movement West: $5$ km
- Net East-West Displacement = $2 \text{ km (West)} + 5 \text{ km (West)} = 7 \text{ km (West)}$.
So, Rakesh's final position is $7$ km directly West of his home.
Determining the Shortest Distance
The shortest distance between two points is a straight line. Since Rakesh's net North-South displacement is $0$ km, his final position is horizontally aligned with his home. The entire displacement is along the East-West axis.
Therefore, the shortest distance between Rakesh's final position and his home is the net East-West displacement.
Shortest Distance = Net East-West Displacement = $7$ km.
Important Questions from Direction and Distance (Notes)
- If a map is placed in such a manner that east becomes southeast, then what will northeast become?
Point A is $30$ m to the North of point B. Point A is $10$ m to the west of point C. Point C is $20$m to the North of point D. Point E is $20$ m to the East of point D. Point F is $20$ m to the South of point E. What is the shortest distance from the point B to point E.
- The door of Aman's house faces east. From the back side of his house, Aman walks straight 30m. Again he walks 20m after turning to his left, then he turns to his right and walks 30m. Finally he turn towards north and walks 20m and stops. So, what is the distance between the starting and the end point?
- Smitha runs 10 km south from her flat, turns left and walks 23 km again turns left and walks 40 km then turns right and walks 5 km to reach her office. In which direction is the office from her house?
I starts from Point A and drives 5 km towards the north. He then takes a right turn, drives 2 km, turns right and drives 9 km. He then takes a right turn and drives 7 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are $90^\circ$ turns only unless specified.)
