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One man started to 25m north then 25m right and 50m next right.What will be the distance from his initial point

Question

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Solution

The man's movement can be broken down into three steps:

  1. He starts by moving 25m north.
  2. Then he turns right and moves 25m. In the context of his initial direction (north), moving right means moving east.
  3. Then he takes another right turn and moves 50m. In the context of his current direction (east), moving right means moving south.

So, at the end of his movement, he is 25m east and 25m south of his starting point.

We can use the Pythagorean theorem to calculate the straight-line distance from his final position to his starting point. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here, the two sides of the triangle are the eastward distance and the southward distance, and the hypotenuse is the straight-line distance from the starting point to the final position.

So, the square of the distance is (25m)^2 + (25m)^2 = 625m^2 + 625m^2 = 1250m^2.

Taking the square root of both sides to solve for the distance, we get that the distance is sqrt(1250m^2) = 35.36m.

So, the man is approximately 35.36m away from his starting point.

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