Directional Movement Analysis
Let's track Nilesh's movement relative to his starting point Y, considering North as the positive y-axis and East as the positive x-axis.
- Starts at Point Y: Coordinates (0, 0).
- Drives 17 km North: Position (0, 17).
- Turns left (West) and drives 31 km: Position (0 - 31, 17) = (-31, 17).
- Turns left (South) and drives 45 km: Position (-31, 17 - 45) = (-31, -28).
- Turns right (West) and drives 23 km: Position (-31 - 23, -28) = (-54, -28).
- Turns right (North) and drives 28 km: Position (-54, -28 + 28) = (-54, 0).
- Nilesh stops at Point Z, located at coordinates (-54, 0) relative to Y.
Calculating Return Journey to Point Y
Point Z is at (-54, 0) and Point Y is at (0, 0).
To find the shortest distance and direction from Z to Y:
- The net displacement from Y to Z is 54 km in the West direction (due to the negative x-coordinate).
- Therefore, to return from Z to Y, Nilesh needs to travel in the opposite direction.
- Distance calculation: The distance is the magnitude of the displacement vector from Z to Y, which is $\sqrt{(0 - (-54))^2 + (0 - 0)^2} = \sqrt{54^2} = 54$ km.
- Direction: Driving East from Z will bring Nilesh back to Y.
Nilesh needs to drive 54 km towards the East to reach Point Y again.
Similar Questions
- Tina starts from Point Y and drives 4 km towards north. Then, she takes a left turn and drives 2 km, she turns left again and drives 6 km. She then takes a left turn and drives 4 km. Then, she turns right and drives 4 km. She then takes a final right turn and drives 2 km and stops at Point Z. How far (shortest distance) and towards which direction should she drive in order to reach Point Y again? (All turns are 90-degree turns only, unless specified.)
- Xheik starts from Point A and drives 18 km towards East. He then takes a left turn, drives 4 km, turns left and drives 21 km. He then takes a left turn and drives 9 km. He takes a final left turn, drives 3 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° turns only unless specified.)
- A wristwatch reads 7.30 am. If the hour hand points south-west, then in what direction will the minute hand point after 15 minutes?
- Vignesh starts from Point Y and drives 17 km towards south. He then takes a left turn, drives 25 km. He then turns right and drives 9 km. He takes a final right turn, drives 25 km and stops at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90° turns only unless specified.)
- Read the given paragraph carefully and answer the question.
Ram walks 5 km straight from his home. After taking a right turn he walks for another 8 km. He then takes a left turn and reaches shop A after 2 km. From there he takes a right turn and walks 2 km. He covers another 7 km to the right to reach shop B.
What is the distance covered by Ram to reach shop A from his home? Jack is walking on Light Street and can see the Regal Café to his left. What direction is Jack facing?
Jai leaves his home and turns towards the east on to Bank Street. He walks two blocks and then turns towards the south. He continues until the end of the road. Jai is closest to which of the following?
- Pallavi walked from her college library, 70 m towards the north, then 60 m towards the east, then 45 m towards the north and then 60 m towards the west. She stopped at this point to buy some candies from a candy shop. She again walked 50 m towards the north. How far and in which direction is Pallavi's college library from the candy shop?
- A man walks 10 m forward towards the direction of sunrise and then 10 m to his right. After that, every time turning to his left, he walks 5 m, 15 m and 15 m, respectively. What is the likely direction he is in now with reference to his starting point?
- Jagdish, from his house, ran 200 steps towards the east and then ran 40 steps after turning to his right to reach a tea stall. He then ran 40 steps towards his right and reached a bus stop. He then, turned towards his right and ran 40 steps. From there, turning towards his right he ran 140 steps and reached a post office.
How far and in which direction is the post office with respect to Jagdish's house?
Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
