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Zorluk: OrtaDirection and Distance Test

At 7:00 AM, a courier agent stands at a distribution hub such that his shadow falls directly to his right side. He walks 12 m12\text{ m} straight ahead, turns 135∘135^\circ anti-clockwise, and walks 102 m10\sqrt{2}\text{ m}. He then turns 45∘45^\circ clockwise and walks 14 m14\text{ m}. Finally, he turns 90∘90^\circ to his right and walks 10 m10\text{ m} to reach his final destination. What is his shortest distance and direction from the starting point?

  1. 36 m36\text{ m}, SouthCevap
  2. B
    36 m36\text{ m}, North
  3. C
    34 m34\text{ m}, South
  4. D
    102 m10\sqrt{2}\text{ m}, South-East

Cevap

36 m36\text{ m} due South
At 7:00 AM (sunrise), the sun is in the East, projecting shadows toward the West. For a person's shadow to fall to their right, West must be to their right, which means they are facing South. Moving 12 m12\text{ m} South, turning 135∘135^\circ anti-clockwise (facing South-East) for 102 m10\sqrt{2}\text{ m} adds 10 m10\text{ m} East and 10 m10\text{ m} South. Turning 45∘45^\circ clockwise (facing South) for 14 m14\text{ m} adds 14 m14\text{ m} South. Turning 90∘90^\circ right (facing West) for 10 m10\text{ m} subtracts 10 m10\text{ m} East. The net East-West displacement is 10−10=0 m10 - 10 = 0\text{ m}, and the net North-South displacement is −12−10−14=−36 m-12 - 10 - 14 = -36\text{ m} (South). Thus, the agent is 36 m36\text{ m} due South.

Adım Adım Çözüm

1
Determine initial facing direction using shadow orientation at sunrise.
Initial facing direction is South.
At 7:00 AM, the sun rises in the East, so shadows fall toward the West. Since the shadow is to the agent's right, West is to his right, meaning he faces South.
2
Trace Movement 1: Walk 12 m12\text{ m} straight ahead.
Displacement: (0,−12) m(0, -12)\text{ m} relative to origin (0,0)(0,0). Facing South.
Walking straight ahead from South orientation moves him 12 m12\text{ m} South.
3
Trace Movement 2: Turn 135∘135^\circ anti-clockwise and walk 102 m10\sqrt{2}\text{ m}.
Displacement: +10 m+10\text{ m} East, −10 m-10\text{ m} South. Cumulative position: (+10,−22) m(+10, -22)\text{ m}. Facing South-East.
Turning 135∘135^\circ anti-clockwise from South reorients him toward South-East. 102cos⁡(45∘)=10 m10\sqrt{2} \cos(45^\circ) = 10\text{ m} East and 102sin⁡(45∘)=10 m10\sqrt{2} \sin(45^\circ) = 10\text{ m} South.
4
Trace Movement 3: Turn 45∘45^\circ clockwise and walk 14 m14\text{ m}.
Displacement: −14 m-14\text{ m} South. Cumulative position: (+10,−36) m(+10, -36)\text{ m}. Facing South.
Turning 45∘45^\circ clockwise from South-East reorients him to face South.
5
Trace Movement 4: Turn 90∘90^\circ right and walk 10 m10\text{ m}.
Displacement: −10 m-10\text{ m} West. Final position: (0,−36) m(0, -36)\text{ m}.
Turning right from South reorients him to face West. Walking 10 m10\text{ m} West cancels out the +10 m+10\text{ m} East component.
6
Calculate final net distance and direction from starting point (0,0)(0,0).
Distance = 36 m36\text{ m}, Direction = South.
Net coordinates (0,−36)(0, -36) indicate a location 36 m36\text{ m} due South of origin.

Anahtar Kavram

Combining shadow-based initial orientation with multi-step directional vector displacement and angular rotations.

Daha Fazla Pratik

Practice similar questions where shadow direction at sunset (5:00 PM) is used to find initial orientation.

Alternatif Yöntem

Use a standard Cartesian coordinate system (x,y)(x,y) with North as +y+y, South as −y-y, East as +x+x, and West as −x-x. Setting origin at (0,0)(0,0) and tracking coordinates step-by-step: (0,−12)→(0+10,−12−10)=(10,−22)→(10,−22−14)=(10,−36)→(10−10,−36)=(0,−36)(0, -12) \rightarrow (0+10, -12-10) = (10, -22) \rightarrow (10, -22-14) = (10, -36) \rightarrow (10-10, -36) = (0, -36), yielding 36 m36\text{ m} South directly.
Tahmini Süre:1m 30s
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Direction and Distance Test

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