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.

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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asked 2021-04-06
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.

Answers (1)

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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