Read the following information to answer the given question. Starting from…

2024

Read the following information to answer the given question.

Starting from point A, Jackie Chan walked 50 m towards the west. He turned left and walked 20 m and did a somersault.

He then turned left and walked 50 m and did a backflip. After this, he turned to his right and walked 10 m. How far and in which direction is Jackie Chan from A?

Answer: A. 30 m, SouthConcept: In direction-sense problems, resolve the path into net displacement along two perpendicular axes — East-West and North-South — rather than adding the…

  1. A.

    30 m, South

  2. B.

    30 m, North

  3. C.

    40 m, South

  4. D.

    40 m, North

Show answer & explanation

Correct answer: A

Concept: In direction-sense problems, resolve the path into net displacement along two perpendicular axes — East-West and North-South — rather than adding the raw path length. A left turn rotates the facing direction 90° counter-clockwise (North → West → South → East → North), and a right turn rotates it 90° clockwise (North → East → South → West → North). When two legs on the same axis are equal and opposite, they cancel completely, so the remaining legs on the other axis add directly to give the straight-line distance from the start.

Application:

  1. Start at A, facing west. Walk 50 m west to reach B (net so far: 50 m west of A).

  2. At B, turn left: facing west, a left turn points south. Walk 20 m south to reach C (net: 50 m west, 20 m south of A).

  3. At C, turn left again: facing south, a left turn points east. Walk 50 m east to reach D — this exactly cancels the earlier 50 m west leg, so D lies directly south of A, 20 m south.

  4. At D, turn right: facing east, a right turn points south. Walk 10 m south to reach E. D and E both lie on the same north-south line through A, so the southward legs add: 20 m + 10 m = 30 m south of A.

Cross-check (coordinates, east = +x, north = +y, A = (0, 0)): B = (-50, 0) after the west leg; C = (-50, -20) after the south leg; D = (0, -20) after the east leg — D shares A's x-coordinate, matching the diagram's dashed vertical line through A and D; E = (0, -30) after the final south leg. The straight-line distance from A(0, 0) to E(0, -30) is 30 m due south, confirming the option "30 m, South".

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