You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-140 m, 30 m). the x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (b_x and -70), then (-20 and c_y), then (-60 and -70). what are (a) component b_x and (b) component c_y? what are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

a) b_x = -80 [m]

b) c_y = 110 [m]

c) 143.18 [m]

d) 167.9 deg

Step-by-step explanation:

1) Draw a xy coordinate system

2) Locate the two known points which are 1 and 4

3) From point 1 you will move (x=b_x and y=-70), but you don´t know what b_x is, all you can do is move in y the known quantity of -70, from here you can draw a horizontal line as your point 2 will fall somewhere in this horizontal line.

4) To get to point 4 you moved (x=-60, y=-70), this means that you can move in the positive direction from point 4 to get to point 3 and you find that point 3 is located in (x=-80, y=100)

5) You also know that in order to get to point 3, you moved (x=-20, y=c_y= from point 2. So you can move 20 to the positive direction from point 3 and draw a vertical line. The vertical line will intersect with the horizontal line you drew in step 3. The intersection is the location of point 2 and it is (x=-60, y=-10)

6) Now we can figure out what quantities correspond to b_x and c_y. From point 1 you moved (x=-80, y=-70) thus b_x=-80. From point 2, you moved (x=-20, y=110) thus c_y =110

9) To get the magnitude of the overall displacement we first need to know what is the overall displacement and it was given to us since the beggining. We know the initial position and the final position. The overall displacement is our position change from beggining to end. All we need to do is draw a vector from the initial position to the final position. We can see that it moves 140m horizontally and 30m vertically.

10) Use the pythagoras theorem to get the hypotenuse of the triangle rectangle formed by 140m base and 30m height.

11) Get the angle relative to the positive direction of x axis: