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183_notes:examples:vectordecomposition [2014/07/10 19:06] – [Solution] caballero | 183_notes:examples:vectordecomposition [2014/07/10 19:08] (current) – [Solution] caballero | ||
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- | The angle that you know ($\theta = 35^{\circ}$) is the one that the vector makes with the negative y-axis. So the opposite side is the $x$-component. Hence, | + | The angle that you know ($\theta = 35^{\circ}$) is the one that the vector makes with the negative y-axis. So the opposite side is the $x$-component. Hence the above formula do not apply and, |
$$ r_x = |\vec{r}| \sin(\theta) = (5\:m) \sin(35^{\circ}) = 2.87\:m$$ | $$ r_x = |\vec{r}| \sin(\theta) = (5\:m) \sin(35^{\circ}) = 2.87\:m$$ | ||
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+ | The $y$-component is the adjacent side and is negative. Hence, | ||
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+ | $$ r_y = -|\vec{r}| \cos(\theta) = -(5\:m) \cos(35^{\circ}) = -4.10\:m$$ | ||
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+ | where the minus sign was introduced because the measure of the angle was less than 90$^{\circ}$. |