Sharad starts from Point Y and drives 9 km towards the South. He then takes a left turn, drives 19 km, turns right and drives 23 km. He then takes a right turn and drives 8 km. He takes a right turn and drives 17 km. He then turns left, drives 11 km, turns left and drives 6 km to stop 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 degrees turns only unless specified)
21 km towards the north
Solving Directional Movement: Point Y to Point Z Journey
This problem involves tracking a series of movements in different directions to find the final displacement. We need to determine the shortest distance and direction from the final point (Point Z) back to the starting point (Point Y).
Tracking Sharad's Movement Details
Let's track Sharad's position step-by-step. We can use a coordinate system where Point Y is the origin (0, 0). We'll consider North as the positive y-axis, South as the negative y-axis, East as the positive x-axis, and West as the negative x-axis.
| Step | Direction of Movement | Distance (km) | Change in X | Change in Y | Position (X, Y) | Current Facing Direction |
| Start | - | - | 0 | 0 | (0, 0) (Point Y) | - |
| 1 | South | 9 | 0 | -9 | (0, -9) | South |
| 2 | East (Left Turn) | 19 | +19 | 0 | (19, -9) | East |
| 3 | South (Right Turn) | 23 | 0 | -23 | (19, -32) | South |
| 4 | West (Right Turn) | 8 | -8 | 0 | (11, -32) | West |
| 5 | North (Right Turn) | 17 | 0 | +17 | (11, -15) | North |
| 6 | West (Left Turn) | 11 | -11 | 0 | (0, -15) | West |
| 7 | South (Left Turn) | 6 | 0 | -6 | (0, -21) (Point Z) | South |
Calculating Net Displacement to Return to Point Y
The final position is Point Z at coordinates (0, -21). The starting position was Point Y at (0, 0).
To return from Point Z to Point Y, we need to calculate the required change in coordinates:
- East-West Displacement (\(\Delta x\)): Required change in x = x-coordinate of Y - x-coordinate of Z = \(0 - 0 = 0\) km.
- North-South Displacement (\(\Delta y\)): Required change in y = y-coordinate of Y - y-coordinate of Z = \(0 - (-21) = +21\) km.
A displacement of \(+21\) km in the y-direction means moving 21 km towards the North.
Final Distance and Direction Calculation
The journey back from Point Z to Point Y requires a net movement of 0 km horizontally (East-West) and 21 km vertically (North).
The shortest distance is calculated using the Pythagorean theorem, based on the net displacements:
Shortest Distance \(= \sqrt{(\Delta x)^2 + (\Delta y)^2}\)
Shortest Distance \(= \sqrt{(0 \text{ km})^2 + (21 \text{ km})^2}\)
Shortest Distance \(= \sqrt{0 + 441 \text{ km}^2}\)
Shortest Distance \(= \sqrt{441 \text{ km}^2}\)
Shortest Distance \(= 21 \text{ km}\)
The direction associated with the net displacement of +21 km in the y-axis is North.
Therefore, to reach Point Y again from Point Z, Sharad should drive 21 km towards the North.
Similar Questions
- Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 km. He takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
- A taxi travels 7 km south, then turns towards the east and travels 5 km, then turns towards the north and travels 7 km and then turns to its left and travels 2 km. What is the location of the taxi now with respect to its starting position?
- Two fielders, I and J, start from the same point on a ground. I runs 20 m north and then turns towards the east and runs 35 m. He then turns to his right and runs 15 m. Meanwhile, J runs 30 m north and then turns right and runs 35 m. Where is J now with respect to I?
- A man walks 6 km towards north and turns left and walks 2 kms towards West. If he has started from point Z and reached point A, then what is the shortest distance between point Z and A.
- A village girl walks 3 km east starting from her home in search of water. She then turns south and walks 2 km, then she turns east and walks 7 km, then she turns to her left and walks 2 km. Where is her home with respect to her position now?
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- Two fielders, I and J, start from the same point on a ground. I runs 20 m north and then turns towards the east and runs 35 m. He then turns to his right and runs 15 m. Meanwhile, J runs 30 m north and then turns right and runs 35 m. Where is J now with respect to I?
A man starts from ‘O’, travels 20 km towards East to reach point ‘A’, turns right and travels 10 km to reach point ‘B’, turns right and travels 9 km to reach point ‘C’, turns right and travels 5 km to reach point ‘D’, turns left and travels 11 km and stops for some time and travels 1 km to reach point ‘E’ and then turns right and travels 6 km to reach point ‘F’.
What is the shortest distance between point ‘A’ and point ‘D’?In the morning X and Y are walking towards each other in a park. When they meet, Y's shadow' falls upon X. In which direction was X facing?
Two workers K and L start walking from the same point. K walks 5 km North, then turns right and walks 2 km. Meanwhile, L walks 3 km West, then turns South and walks 4 km. Finally L turns left and walks 5 km. Where is K with respect to L?
Important Questions from Direction and Distance
- Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 km. He takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
- Town Q is to the east of Town P. Town R is to the south of Town Q. Town S is to the east of Town R. Town T is to the south of Town S. Town U is to the east of Town T. What is the position of Town U with respect to Town Q?
- Binoy starts from Point Y and drives 16 km towards the north. He then takes a right turn and drives 43 km, then turns right and drives 38 km. He then takes a right turn and drives 19 km. He takes a final right turn, drives 22 km and stops at Point Z. How far (shortest distance) and in which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified.)
- Himank starts from Point A and drives 13 km towards West. He then takes a left turn, drives 3 km, turns left and drives 16 km. He then takes a left turn and drives 6 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.)
- Shyam starts from Point A and drives 12 km towards east. He then takes a right turn,
drives 7 km, turns right and drives 5 km. He then takes a left turn and drives 9 km. He
takes a final right turn, drives 7 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.)
