Binoy's Journey: Step-by-Step Movement Analysis
This problem involves tracking a series of movements in cardinal directions to find the final displacement and determine the path back to the starting point. We can visualize Binoy's journey on a 2D plane, assuming Point Y is the origin (0, 0).
Let's track Binoy's position:
- Starting Point: Point Y at coordinates (0, 0).
- Movement 1: Drives 16 km towards the north.
- Current Position: (0, 16).
- Movement 2: Takes a right turn (now facing East) and drives 43 km.
- Current Position: (0 + 43, 16) = (43, 16).
- Movement 3: Turns right (now facing South) and drives 38 km.
- Current Position: (43, 16 - 38) = (43, -22).
- Movement 4: Takes a right turn (now facing West) and drives 19 km.
- Current Position: (43 - 19, -22) = (24, -22).
- Movement 5: Takes a final right turn (now facing North) and drives 22 km.
- Final Position (Point Z): (24, -22 + 22) = (24, 0).
Calculating Binoy's Final Position (Point Z)
After completing all the movements, Binoy stops at Point Z. His final coordinates are (24, 0).
Point Y was the starting point at (0, 0).
Point Z is located 24 km east of the starting point Y along the x-axis, and at the same north-south level as Y.
Determining the Return Path to Point Y
To find the shortest distance and direction from Point Z back to Point Y, we need to calculate the displacement vector from Z to Y.
- Current Location: Point Z (24, 0).
- Destination: Point Y (0, 0).
The displacement vector $\vec{ZY}$ is calculated as:
$\vec{ZY} = Y - Z = (0 - 24, 0 - 0) = (-24, 0)$
This vector indicates the required movement:
- The x-component is -24, meaning a movement of 24 km in the negative x-direction (West).
- The y-component is 0, meaning no movement in the north-south direction is needed.
The shortest distance is the magnitude of this displacement vector:
Distance $= \sqrt{(-24)^2 + (0)^2} = \sqrt{576} = 24$ km.
The direction is determined by the vector components. Since the movement is entirely along the negative x-axis, the direction is towards the West.
Conclusion: Path from Point Z to Point Y
Binoy needs to travel 24 km towards the west to reach Point Y again from Point Z.
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?
- 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.) - Babar starts from Point A and drives 14 km towards West. He then takes a left turn,
drives 7 km, turns right and drives 9 km. He then takes a right turn and drives 7 km. He
takes a final right turn, drives 5 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.)
