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Sonu walked 25 m towards south and then took a left turn and walked 45 m. Again he took a left turn and walked 25 m. Finally he turned to his right and walked 20 m and stopped. How far and in which direction is Sonu from starting point?

Mathematics

ScanSolve AI Answer

Answer

65 m, East\text{65 m, East}

Step-by-step solution

3 steps
  1. Define the starting point and directions.

    Let the starting point be the origin $(0,0)$.
    North is in the positive y-direction.
    South is in the negative y-direction.
    East is in the positive x-direction.
    West is in the negative x-direction.

  2. Trace Sonu's movements.

    • Sonu walked 25 m towards south. Current position: (0,−25)(0, -25). Direction: South.

    • Then took a left turn and walked 45 m. From South, a left turn is East. Movement: 45 m East. Current position: (0+45,−25)=(45,−25)(0 + 45, -25) = (45, -25). Direction: East.

    • Again he took a left turn and walked 25 m. From East, a left turn is North. Movement: 25 m North. Current position: (45,−25+25)=(45,0)(45, -25 + 25) = (45, 0). Direction: North.

    • Finally he turned to his right and walked 20 m. From North, a right turn is East. Movement: 20 m East. Current position: (45+20,0)=(65,0)(45 + 20, 0) = (65, 0). Direction: East.

  3. Determine the final distance and direction from the starting point.

    The final position is (65,0)(65, 0).
    The starting point was (0,0)(0,0).
    The distance from the starting point is the magnitude of the displacement vector from (0,0)(0,0) to (65,0)(65,0).

    Distance=(65−0)2+(0−0)2=652=65 m\text{Distance} = \sqrt{(65-0)^2 + (0-0)^2} = \sqrt{65^2} = 65 \text{ m}

    Since the final position is (65,0)(65,0), which is along the positive x-axis relative to the origin, the direction is East.

    Sonu is 65 m, East\boxed{\text{65 m, East}} from the starting point.

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