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Oksi-84 [34.3K]
3 years ago
11

Suppose you first walk 12.0 m in a direction 20 owest of north and then 20.0 m in a direction 40.0osouth of west. How far are yo

u from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , then this problem asks you to find their sum R = A + B . The two displacements A and B add to give a total displacement R having magnitude R and direction in degrees.

Physics
1 answer:
alexgriva [62]3 years ago
6 0

Answer:

R=19.5m

\theta = 4.65° S of W

Explanation:

Refer the attached fig.

displacement  of the x and y components

x-component displacement is (R_{x}) = A_{x}+B_{x}

= A \sin(20°) + B \cos(40°)

= -12.0\sin(20°) + 20.0\cos(40°)

= -19.425m

x-component displacement is (R_{y}) = A_{y}+ B_{y}

=  A \cos(20°) - B \sin(40°)

= 12.0\cos(20°) - 20.0\sin(40°)

= -1.579

resultant displacement

∴

R = \sqrt{R_{x}^{2} +R_{y}^{2} }  }

=\sqrt{(-19.425)^{2}+(-1.579)^{2}  }

=19.5m

\theta = \tan^{-1}\left | \frac{R_{x}}{R_{y}} \right |

\theta = \tan^{-1}\left | \frac{1.579}{19.425} \right |

\theta = 4.65° S of W

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