a body moves in such a way that has a dislacement of 12m towards east,5m towards the north and then 9m vertically upwards. compute the magnitude of its resultant displacement.
To compute the magnitude of the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we can consider the displacement in the horizontal (east-west) plane as one side of the triangle, the displacement in the vertical (up-down) plane as the other side, and the resultant displacement as the hypotenuse.
Given:
Displacement towards east = 12 m
Displacement towards north = 5 m
Vertical displacement upwards = 9 m
To find the magnitude of the resultant displacement, we can set up the equation:
Resultant Displacement^2 = (Displacement towards east)^2 + (Displacement towards north)^2 + (Vertical displacement upwards)^2
Substituting the given values:
Resultant Displacement^2 = 12^2 + 5^2 + 9^2
Simplifying:
Resultant Displacement^2 = 144 + 25 + 81
Resultant Displacement^2 = 250
Taking the square root of both sides, we get:
Resultant Displacement = √250
Calculating the square root of 250, we find:
Resultant Displacement ≈ 15.811 meters
Therefore, the magnitude of the resultant displacement is approximately 15.811 meters.
what is
sqrt(12^2+5^2+9^2) ?