Question

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 (-174 m, 38 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). What are (a) component bx and (b) component cy

Answer 1

Explanation:

Starting point is (0,0)

ending point is (-174,38)

There are 4 moves

(20,60)

(bx,-70)

(-20,cx) and (-60,-70)

Take a vector between the starting and ending point

Vector
`V=<-174,38>`

Vectors for 4 moves are

`V_l=<20,60>\\V_2=<bx,-70>\\V_3=<-20,cy>\\V_4=<-60,-70>`

V is the addition of 4 vectors

`V=V_1+V_2+V_3+V_4\\V=<20+bx-20-60, 60-70+cy-70>\\V=<bx-60,cy-80>`

Now we replace vector V

`V=<bx-60,cy-80>\\<-174,38>=<bx-60,cy-80>\\bx-60=-174\\bx=-114\\cy-80=38\\cy=118`

component bx is -114

component cy is 118