Question

The 1st leg of my trip I walk da = 105 m at A= 25° south of east. The 2nd leg of my trip I dB = 125 m at B = 15° north of east. On my final leg I walk dc = 95 m at c = 61.5° north of west. Choose the coordinate syst so that x is directed towards the east, and y is directed towards the north.

Write an expression for the x-component of the final displacement in terms of the given quantities.
Rₓ = ____

Answer 1

The x-component of the final displacement Rx is calculated as 95 m multiplied by the cosine of 28.5 degrees, obtained by subtracting the given angle from 90 degrees to account for the direction north of west.

Step-by-step explanation:

To find the expression for the x-component of the final displacement in terms of the given quantities:

We are given that for the final leg of the trip, the displacement is dc = 95 m at C = 61.5° north of west. The coordinate system is set such that x is directed towards the east, and y is directed towards the north.

To find the east (x) component of this displacement, we use the cosine function since it gives us the adjacent side of the triangle (which corresponds to the x-axis in our coordinate system), with the angle measured from the west direction towards north. However, because the angle is given north of west and we need the angle east of north (to use the cosine correctly), we subtract the angle from 90°.

Rx = dc × cos(90° - C)

Rx = 95 m × cos(90° - 61.5°) = 95 m × cos(28.5°)

So, the x-component of the final displacement Rx is 95 m multiplied by the cosine of 28.5 degrees.