Four Moves You are to make four straight-line moves over a flat desert floor, st

Question

Four Moves 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 (-135 m, 40 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 (-63 and -75)

(a) What is component bx?

(b) What is component cy?

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

(d) What is the angle (relative to the positive direction of the x axis)?

Explanation / Answer

(a) 20 + bx - 20 - 63 = -135 ==> bx = -72 (b) 60 - 70 + cy - 75 = 40 ==> cy = 125 (c) magnitude = [ (-135)^2 + (40)^2]^1/2 = 140.80 m (d) direction = tan-1(40 / -135) = - 16.50 deg or 343.49 deg

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