Simar starts from Point A and drives 10 km towards south. He then takes a right turn, drives 7 km, turns right and drives 12 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 2 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 determine the distance and direction from Point P back to Point A, we need to trace Simar's movements and find the net displacement.
Tracing Simar's Driving Route
Let's assume the starting Point A is at the origin (0, 0) on a coordinate plane, with North being the positive y-axis and East being the positive x-axis.
- Movement 1: Drives 10 km South. New position: (0, -10).
- Movement 2: Turns right (facing West) and drives 7 km. New position: (-7, -10).
- Movement 3: Turns right (facing North) and drives 12 km. New position: (-7, -10 + 12) = (-7, 2).
- Movement 4: Turns right (facing East) and drives 9 km. New position: (-7 + 9, 2) = (2, 2).
- Movement 5: Turns right (facing South) and drives 2 km. New position: (2, 2 - 2) = (2, 0). This is the final Point P.
Calculating Return Path to Point A
Simar's final position is Point P at (2, 0). The starting Point A is at (0, 0).
- To return to Point A (0, 0) from Point P (2, 0), Simar needs to change his x-coordinate from 2 to 0 and keep his y-coordinate at 0.
- The change in the x-coordinate is $0 - 2 = -2$. A negative change in the x-coordinate represents movement towards the West.
- The change in the y-coordinate is $0 - 0 = 0$. There is no North or South movement required.
- The distance is the magnitude of the change along the x-axis, which is $|-2|$ km = 2 km.
- The direction is West.
Therefore, Simar needs to drive 2 km to the west to reach Point A again.
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?
