You are to make four straight-line moves over a flat desert floor,starting at th

Question

You are to make four straight-line moves over a flat desert floor,starting at the origin of an xy coordinate system andending at the xy coordinates (-135 m, 40 m). The xcomponent and y component of your moves are the following,respectively, in meters: (20 and 60), then (bx and -70),then (-20 and cy), then (-63 and-71). (a) What is component bx?
1 m

(b) What is component cy?
2 m

(c) What is the the magnitude of the overall displacement?
3 m

(d) What is the angle of the overall displacement?
4° (counterclockwise from the positivex axis) (a) What is component bx?
1 m

(b) What is component cy?
2 m

(c) What is the the magnitude of the overall displacement?
3 m

(d) What is the angle of the overall displacement?
4° (counterclockwise from the positivex axis)

Explanation / Answer

Part A) look at the x-components: -135=20+Bx-20-63 Bx=-72m Part B) look at the y-components: 40=60-70+Cy-71 Cy=121m Part C) find the resultant: Rx=-135 Ry=40 |R|=(Rx2+Ry2)=140.8m Part D) use trigonometry to find the angle: =tan-1(Ry/Rx)=-16.50o remember that the inverse tangent function only gives anglesbetween 90 and -90 (1st and 4th quadrants). so you alwaysneed to look at the components Rx and Ry to see if you found thecorrect angle or if you need to add 180 degrees to it. SinceRx is negative and Ry is positive, the angle is actually in the 2ndquadrant, not the 4th: =-16.50+180=163.50o

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