# A man lost in a maze makes three consecutive displacements so that at the end of his travel he is right back where he started. The first displacement is 4.00 m westward, and the second is 10.0 m northward. Use the graphical method to find the magnitude and direction of the third displacement.

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A man lost in a maze makes three consecutive displacements so that at the end of his travel he is right back where he started. The first displacement is 4.00 m westward, and the second is 10.0 m northward. Use the graphical method to find the magnitude and direction of the third displacement.

2021-04-08
To find the magnitude of the third displacement, use the Pythagorean Theorem
$$\displaystyle{C}^{{2}}={A}^{{2}}+{B}^{{2}}$$
$$\displaystyle{C}^{{2}}={4}^{{2}}+{10}^{{2}}$$
$$\displaystyle{C}={10.8}{m}$$
To find the direction, use $$\displaystyle{\tan{\theta}}={\frac{{{4}}}{{{10}}}}$$
$$\displaystyle\theta={a}{r}{c}{t}{a}{b}{\left({\frac{{{4}}}{{{10}}}}\right)}$$
$$\displaystyle\theta={21.8}$$ degrees east of south

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