Four athletes are training on a large flat ground. Match each athlete's movement sequence … — State PSC Exam

Four athletes are training on a large flat ground. Match each athlete's movement sequence with their final direction relative to their respective starting points.

Athlete P: Runs $30\text{ m}$ North, turns right to run $40\text{ m}$ , then turns right again and runs $30\text{ m}$ .East
Athlete Q: Runs $50\text{ m}$ South, turns left to run $20\text{ m}$ , then turns left again and runs $70\text{ m}$ .North-East
Athlete R: Runs $40\text{ m}$ West, turns right to run $40\text{ m}$ , then turns left and runs $20\text{ m}$ .North-West
Athlete S: Runs $60\text{ m}$ East, turns right to run $50\text{ m}$ , then turns right again and runs $80\text{ m}$ .South-West

Answer

Athlete P matches with East, Athlete Q matches with North-East, Athlete R matches with North-West, and Athlete S matches with South-West.

By placing each athlete's starting point at an origin

(0,0)

on a Cartesian plane, their movements can be translated into coordinate updates. P ends at

(40, 0)

which is East. Q ends at

(20, 20)

which is North-East. R ends at

(-60, 40)

which is North-West. S ends at

(-20, -50)

which is South-West.

Step-by-Step Solution

Calculate final position of Athlete P.

Starts at

(0,0)

. Moves to

(0, 30)

after going North, then to

(40, 30)

after running East, and finally down to

(40, 0)

after running South.

Tracking coordinates simplifies finding the final direction. The point

(40, 0)

lies exactly on the positive x-axis, meaning the direction is East.

Calculate final position of Athlete Q.

Starts at

(0,0)

. Moves to

(0, -50)

after going South. A left turn from South faces East, moving to

(20, -50)

. Another left turn faces North, moving

70\text{ m}

(20, 20)

The final point

(20, 20)

has positive x (East) and positive y (North) components, placing it in the North-East direction from the origin.

Calculate final position of Athlete R.

Starts at

(0,0)

. Moves to

(-40, 0)

after going West. A right turn from West faces North, moving to

(-40, 40)

. A left turn faces West, moving to

(-60, 40)

The final point

(-60, 40)

has a negative x (West) and positive y (North) component, placing it in the North-West direction.

Calculate final position of Athlete S.

Starts at

(0,0)

. Moves to

(60, 0)

after going East. A right turn faces South, moving to

(60, -50)

. Another right turn faces West, moving

80\text{ m}

(-20, -50)

The final point

(-20, -50)

has a negative x (West) and negative y (South) component, placing it in the South-West direction.

Key Concept

Tracking sequential movements using cardinal directions and angular turns to determine net displacement and final relative direction.

Estimated Time:2m 0s

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