Question

A vector w of magnitude 50 points southeast. Resolve the vector into southerly and easterly components.
a) The southerly component has a magnitude of ___.
b)What is the length?

Answer 1

Answer on Question #42008 – Math – Trigonometry

A vector $w$ of magnitude 50 points southeast. Resolve the vector into southerly and easterly components.

a) The southerly component has a magnitude of ___.

b) What is the length?

Solution.

Let input a Cartesian coordinate system with $X$-axis along the south and $Y$-axis along the east. The given vector will be with $\vec{w}(w\cos\alpha; w\sin\alpha)$, there $w = 50$ is the magnitude of the vector and $\alpha = 45{}^{\circ}$ is the angle between the vector and $X$-axis.

a) The southerly component has a magnitude of $|w\cos\alpha| = |50 \cdot \cos 45{}^{\circ}| = 50 \cdot \frac{\sqrt{2}}{2} = 25\sqrt{2}$ points.

b) The projection of the southerly component is $w\cos\alpha = 50 \cdot \cos 45{}^{\circ} = 25\sqrt{2}$.

Answer: a) $25\sqrt{2}$; b) $25\sqrt{2}$.

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