a man walks 12 m due noth , 4 m due east and finally climbs up a vertical pole up to a height of 3 m . find his displacement.

sqrt(12^2 + 4^2 + 3^2) = sqrt 169 = 13 m

why we have to do squares

To find the displacement of the man, we need to consider the net distance traveled in both the horizontal and vertical directions.

First, let's consider the horizontal direction. The man walks 12 m due north and then 4 m due east. Since these two directions are perpendicular to each other, we can use the Pythagorean theorem to find the horizontal distance traveled. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a = 12 m and b = 4 m.

Using the Pythagorean theorem, we have:

c^2 = a^2 + b^2
c^2 = 12^2 + 4^2
c^2 = 144 + 16
c^2 = 160
c ≈ √160
c ≈ 12.65 m

So, the horizontal distance traveled by the man is approximately 12.65 m east.

Next, let's consider the vertical direction. The man climbs up a vertical pole to a height of 3 m. This vertical distance is directly given and doesn't require any calculation.

Finally, we can find the displacement by combining the horizontal and vertical distances. Since distance is a scalar quantity, we need to consider both the magnitude and direction of displacement. The horizontal displacement is 12.65 m east, and the vertical displacement is 3 m upward.

To find the net displacement, we can use vector addition. We add the horizontal displacement vector to the vertical displacement vector using the head-to-tail method.

Drawing a diagram helps visualize this. We can represent the horizontal displacement vector as an arrow pointing to the right with a length of 12.65 units, and the vertical displacement vector as an arrow pointing upwards with a length of 3 units. The net displacement vector would be the straight line distance from the starting point to the ending point of these two vectors.

Using a ruler or a scale, we can measure the length of this net displacement vector on the diagram, which represents the magnitude of the displacement. We can also determine the direction of this vector by measuring the angle it makes with a reference line (usually horizontal).

So, to find the exact displacement (magnitude and direction) of the man, we need to measure it on the diagram using a ruler or a scale.