Answer to Question #248674 in Physics for Idk

Question #248674

Susan hikes 6 miles east, 15 miles north, 1 mile west and 3 miles south. What is her displacement?


1
Expert's answer
2021-10-08T15:43:53-0400

Let's first find xx- and yy-components of the resultant displacement:

dx=6 micos0+15 micos90+1 micos180+3 micos270=5 mi,d_x=6\ mi\cdot cos0^{\circ}+15\ mi\cdot cos90^{\circ}+1\ mi\cdot cos180^{\circ}+3\ mi\cdot cos270^{\circ}=5\ mi,

dy=6 misin0+15 misin90+1 misin180+3 misin270=12 mi.d_y=6\ mi\cdot sin0^{\circ}+15\ mi\cdot sin90^{\circ}+1\ mi\cdot sin180^{\circ}+3\ mi\cdot sin270^{\circ}=12\ mi.

We can find the magnitude of the resultant displacement from the Pythagorean theorem:


d=dx2+dy2=(5 mi)2+(12 mi)2=13 mi.d=\sqrt{d_x^2+d_y^2}=\sqrt{(5\ mi)^2+(12\ mi)^2}=13\ mi.

We can find the direction of the resultant displacement from the geometry:


θ=tan1(dydx),\theta=tan^{-1}({\dfrac{d_y}{d_x}}),θ=tan1(12 mi5 mi)=67.4 N of E.\theta=tan^{-1}({\dfrac{12\ mi}{5\ mi}})=67.4^{\circ}\ N\ of\ E.

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