A particle undergoes three consecutive displacements:and d3 = (-- 13i + 15j) cm. Find the components of theSolution Three-dimensional displacements are more diffi-+ 12k) cm, d, = (23i – 14j -5.0k) cmYour final p(15i + 30jd =the origin.Despitesions, we caresultant displacement and its magnitude.to the carefor vectorcult to imagine than those in two dimensions, because thelatter can be drawn on paper. For this problem, let us concebtualize that you start with your pencil at the origin of a pieceof graph paper on which you have drawn x and y axes. Moveyour pencil 15 cm to the right along the x axis, then 30 cmupward along the y axis, and then 12 cm vertically away fromthe graph paper. This provides the displacement describedby dj. From this point, move your pencil 23 cm to the rightparallel to the x axis, 14 cm parallel to the graph paper inthe -y direction, and then 5.0 cm vertically downward to-ward the graph paper. You are now at the displacementfrom the origin described by d + d9, From this point, movethis moticnized, comR.The reR,= 3Ryour pencil 13 cm to the left in thenally!) 15 cm parallel to the graph paper along the y axis.- x direction, and (fi-Example 3.5 Taking a HikeA hiker begins a trip by first walking 25.0 km southeast fromher car. She stops and sets up her tent for the night. On thesecond day, she walks 40.0 km in a direction 60.0° north ofeast, at which point she discovers a forest ranger's tower.of v25.0Equ(A) Determine the components of the hiker's displacementfor each day.A,Solution We conceptualize the problem by drawing a sketch asin Figure 3.19. If we denote the displacement vectors on thefirst and second days by A and B, respectively, and use the caras the origin of coordinates, we obtain the vectors shown inFigure 3.19. Drawing the resultant R, we can now categorize thisas a problem we've solved before-an addition of two vectors.This should give you a hint of the power of categorizationmany new problems are very similar to problems that we havealready solved if we are careful to conceptualize them.THal

Name: A particle undergoes three consecutive displacements:and d3 = (-- 13i
Uploaded: 2024-03-20T06:57:47.000Z
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Description: A particle undergoes three consecutive displacements:and d3 = (-- 13i + 15j) cm. Find the components of theSolution Three-dimensional displacements are more diffi-+ 12k) cm, d, = (23i – 14j -5.0k) cmYour final p(15i + 30jd =the origin.Despitesions,