How Do You Calculate Resultant Displacement and Direction in Vector Problems?

[redeyes442016]

A person walks the path shown. The total trip consists of four straight-line paths. Note: Figure is not drawn to scale.
a) At the end of the walk, what is the magnitude of the person’s resultant displacement
measured from the starting point? Answer in units of m.
b) What is the direction (measured from duewest, with counterclockwise positive) of the
person’s resultant displacement? Answer in units of ◦.

I attached a pdf with a picture of the diagram. The picture is in number 3
I don't understand how to do the problem, can someone help me get the answer?

 

[jbsteele]

a) The magnitude of the person's resultant displacement is 8 m.b) The direction of the person's resultant displacement is 135° (measured from due west, with counterclockwise positive).

 

[baba89]

a) To determine the magnitude of the person's resultant displacement, we can use the Pythagorean theorem. We know that the person walked four straight-line paths, so we can divide the total trip into two right triangles. The first right triangle has a length of 3 m and a height of 4 m, while the second right triangle has a length of 4 m and a height of 3 m. Using the Pythagorean theorem, we can find the length of the hypotenuse of each triangle, which represents the distance traveled in each path. For the first triangle, the hypotenuse is √(3^2+4^2) = 5 m, and for the second triangle, the hypotenuse is √(4^2+3^2) = 5 m.

To find the total displacement, we can add these two distances together, giving us a total displacement of 10 m. Therefore, the magnitude of the person's resultant displacement is 10 m.

b) To find the direction of the person's resultant displacement, we can use trigonometry. In the first right triangle, the angle opposite the 3 m side is θ, and in the second right triangle, the angle opposite the 4 m side is also θ. Since these two angles are equal, we can use the inverse tangent function to find θ.

tanθ = opposite/adjacent = 4/3
θ = tan^-1(4/3) = 53.13°

This angle represents the direction of the person's displacement from the starting point, measured counterclockwise from due west. Therefore, the person's resultant displacement is 53.13° west of due west.