Figure 4-61 shows the path taken by a drunk skunk over levelground, from initial

Question

Figure 4-61 shows the path taken by a drunk skunk over levelground, from initial point i to final point f.The angles are 1 = 33.0°, 2 =52.0°, and 3 = 76.0°, and the distancesare d1 = 4.80 m, d2 = 7.20m, and d3 = 13.0 m. What are the(a) magnitude and (b) angle ofthe skunk's displacement from i to f? Give theangle as a positive (counterclockwise) or negative (clockwise)angle of magnitude less than 180°, measured from the+x direction. Figure 4-61 shows the path taken by a drunk skunk over levelground, from initial point i to final point f.The angles are 1 = 33.0°, 2 =52.0°, and 3 = 76.0°, and the distancesare d1 = 4.80 m, d2 = 7.20m, and d3 = 13.0 m. What are the(a) magnitude and (b) angle ofthe skunk's displacement from i to f? Give theangle as a positive (counterclockwise) or negative (clockwise)angle of magnitude less than 180°, measured from the+x direction.

Explanation / Answer

   from the given figure the threedisplacements can be written as    d1 =d1 (cos1 i^ + sin1j^)    d2 =d2 [cos(180o + 1 -2) i^ + sin (180o + 1- 2) j^]    d3 =d3 [cos(360o - 3 -2 + 1) i^ + sin(360o - 3 -2 + 1) j^]    the net displacement will be    d= d1 +d2 +d3    the direction will be     = tan-1(dy /dx)       = ........o

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