Question

Find the north and east components of the displacement for the hikers shown in Figure 3.52.

Question Image Figure 3.52: The path of the hikers

East: $3.8 \textrm{ km}$

North: $3.2 \textrm{ km}$

Solution Video

OpenStax College Physics Solution, Chapter 3, Problem 3 (Problems & Exercises) (0:58) Sign up to view this solution video!

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This is College Physics Answers with Shaun Dychko. The east component of the hiker's displacement is the horizontal component of this vector. We find that by taking the length of the vector of five kilometers, multiplying by cosine of this angle between the x component and the vector. So that's five kilometers times cos forty which makes 3.8 kilometers to the east. Then the vertical component is the amount by which they go upwards and this is the opposite leg of this triangle and so to find it, we multiply the hypotenuse which is the length of the displacement vector, by the sine of the angle to find the opposite component. That is the northerly component or the y component. So s subscript y equals s times sine theta which is five kilometers times sine forty which makes 3.2 kilometers to the north.