Atharv starts from Point A and drives 12 km towards west. He then takes a right turn, drives 3 km, turns right and drives 16 km. He then takes a right turn and drives 9 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 degree turns only unless specified.)
To solve the problem, we will track the journey step-by-step and calculate the final position relative to the starting point, Point A.
- Atharv starts from Point A, driving 12 km towards the west. His current position is 12 km west of Point A.
- He then takes a right turn and drives 3 km. A right turn from west points north, thus he is now 3 km north from the last position.
- He turns right again and drives 16 km. A right turn from north faces east, so he drives 16 km east.
- He makes another right turn and drives 9 km. This turn takes him south, and he drives 9 km.
- Finally, he turns right and drives 4 km. This last right turn points him west.
Now, let's summarize the distances north-south and east-west:
- East-West direction: \(12 \text{ km west} - 16 \text{ km east} + 4 \text{ km west} = 0 \text{ km}\) (He returns to the original east-west line).
- North-South direction: \(3 \text{ km north} - 9 \text{ km south} = -6 \text{ km}\)
The net effect is that Atharv is 6 km south of Point A, because of the overall southward travel.
Therefore, to return to Point A, Atharv should travel 6 km to the north.
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
