Four automated field inspection drones execute specific multi-leg navigation routes starti… — State PSC Exam

Four automated field inspection drones execute specific multi-leg navigation routes starting from a central dock at coordinate $(0,0)$ . Match each drone route on the left with its correct final displacement from the starting point on the right.

Route 1: Flies $8\text{ m}$ East, turns $90^\circ$ left to fly $6\text{ m}$ , then turns $135^\circ$ left to fly $6\sqrt{2}\text{ m}$ . $2\text{ m}$ East
Route 2: Flies $5\text{ m}$ West, turns $90^\circ$ right to fly $12\text{ m}$ , then turns $135^\circ$ right to fly $12\sqrt{2}\text{ m}$ . $7\text{ m}$ East
Route 3: Flies $4\text{ m}$ South, turns $90^\circ$ right to fly $7\text{ m}$ , then turns $135^\circ$ right to fly $4\sqrt{2}\text{ m}$ . $3\text{ m}$ West
Route 4: Flies $10\text{ m}$ North, turns $90^\circ$ left to fly $4\text{ m}$ , then turns $135^\circ$ left to fly $10\sqrt{2}\text{ m}$ . $6\text{ m}$ East

Answer

Route 1 matches with 2 m East; Route 2 matches with 7 m East; Route 3 matches with 3 m West; Route 4 matches with 6 m East.

Each route is correctly evaluated by converting consecutive linear displacements and angular turns into 2D Cartesian vectors

(x, y)

. Resolving the diagonal legs (sub-cardinal movements of distance

d\sqrt{2}

) yields horizontal and vertical components of

d

, matching each route to its exact final position relative to the origin.

Step-by-Step Solution

Analyze Route 1 using Cartesian coordinates

Leg 1:

(0,0) \rightarrow (8,0)

. Leg 2:

90^\circ

left turn faces North

\rightarrow (8,6)

. Leg 3:

135^\circ

left turn from North faces South-West. Displacement vector:

(-6, -6)

. Final point:

(8-6, 6-6) = (2,0)

, which is

2\text{ m}

East.

Decompose angular movement into horizontal and vertical vector components.

Analyze Route 2 using Cartesian coordinates

Leg 1:

(0,0) \rightarrow (-5,0)

. Leg 2:

90^\circ

right turn faces North

\rightarrow (-5,12)

. Leg 3:

135^\circ

right turn from North faces South-East. Displacement vector:

(+12, -12)

. Final point:

(-5+12, 12-12) = (7,0)

, which is

7\text{ m}

East.

Calculate position vector after three displacement legs.

Analyze Route 3 using Cartesian coordinates

Leg 1:

(0,0) \rightarrow (0,-4)

. Leg 2:

90^\circ

right turn faces West

\rightarrow (-7,-4)

. Leg 3:

135^\circ

right turn from West faces North-East. Displacement vector:

(+4, +4)

. Final point:

(-7+4, -4+4) = (-3,0)

, which is

3\text{ m}

West.

Calculate net displacement along x-axis from origin.

Analyze Route 4 using Cartesian coordinates

Leg 1:

(0,0) \rightarrow (0,10)

. Leg 2:

90^\circ

left turn faces West

\rightarrow (-4,10)

. Leg 3:

135^\circ

left turn from West faces South-East. Displacement vector:

(+10, -10)

. Final point:

(-4+10, 10-10) = (6,0)

, which is

6\text{ m}

East.

Determine final coordinate offset relative to starting dock.

Key Concept

Vector addition and angular turn resolution in Direction and Distance problems.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic