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Difficulty: MediumDirection and Distance Test

Four marine exploration vessels (Alpha, Beta, Gamma, and Delta) are deployed for oceanographic surveying. Each vessel begins facing a specific cardinal direction and executes a sequence of angular maneuvers as described below:

- Vessel Alpha: Starts facing North, rotates 135∘135^{\circ} clockwise, moves forward, and then rotates 45∘45^{\circ} anti-clockwise.
- Vessel Beta: Starts facing East, rotates 90∘90^{\circ} clockwise, moves forward, and then rotates 135∘135^{\circ} clockwise.
- Vessel Gamma: Starts facing South, rotates 45∘45^{\circ} anti-clockwise, moves forward, rotates 180∘180^{\circ} clockwise, and finally rotates 90∘90^{\circ} anti-clockwise.
- Vessel Delta: Starts facing West, rotates 135∘135^{\circ} anti-clockwise, moves forward, rotates 90∘90^{\circ} clockwise, and finally rotates 45∘45^{\circ} anti-clockwise.

Match each vessel with its final facing direction.

  • Vessel AlphaEast
  • Vessel BetaNorth-West
  • Vessel GammaSouth-West
  • Vessel DeltaSouth

Answer

Vessel Alpha matches with East; Vessel Beta matches with North-West; Vessel Gamma matches with South-West; Vessel Delta matches with South.
Each vessel's final direction is calculated by applying its sequence of clockwise and anti-clockwise rotations mathematically or visually, starting from its initial cardinal direction.

Step-by-Step Solution

1
Calculate the final direction for Vessel Alpha by summing its angular turns from North.
North (0°) + 135° CW - 45° ACW = 90° (East).
Clockwise (CW) turns add to the angle and anti-clockwise (ACW) turns subtract, assuming North is 0° and measuring clockwise.
2
Calculate the final direction for Vessel Beta by summing its angular turns from East.
East (90°) + 90° CW + 135° CW = 315° (North-West).
Tracking successive CW rotations from 90° gives the final orientation on the 360° compass.
3
Calculate the final direction for Vessel Gamma by summing its angular turns from South.
South (180°) - 45° ACW + 180° CW - 90° ACW = 225° (South-West).
Alternating CW and ACW turns are added and subtracted respectively.
4
Calculate the final direction for Vessel Delta by summing its angular turns from West.
West (270°) - 135° ACW + 90° CW - 45° ACW = 180° (South).
Tracking all ACW and CW maneuvers determines the exact final coordinate.

Key Concept

Direction and Distance Test
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Topics

Direction and Distance Test

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