Eb 4.d determine the magnitude and direction of V

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SUMMARY

The discussion focuses on calculating the magnitude and direction of vector V given the components $v_x = -9.80$ units and $v_y = -6.40$ units. The magnitude is determined to be approximately 11.7047 units, while the direction is calculated using the arctangent function, yielding an angle of 33.15 degrees. However, since both components are negative, the correct direction in quadrant III is found by adding 180 degrees, resulting in an angle of 213.15 degrees. The discussion also touches on the use of LaTeX for representing degrees.

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karush
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$\tiny{\\ eb 4.d}$
$\textsf{If $v_x=-9.80$ units and $v_y=-6.40$ units,}\\$
$\textit{determine the magnitude and direction of $V$.}$
\begin{align*}\displaystyle
magnitude&=\sqrt{(-9.8)^2+(-6.4)^2}
=\color{red}{11.7047}\\
direction&=\arctan{\left[\frac{6.4}{-9.8}\right]}
=\color{red}{33.15^o}
\end{align*}

ok the direction is actually in the Q4 but $\arctan{\left[\frac{-6.4}{-9.8}\right]}$
is in Q1! Do we just add $180^o$ for that or is it $-33.15^o$

Also is there symbols for magnitude and direction other than an arrow on the graph

Also where is the latex for degree instead of ^o
 
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karush said:
$\tiny{\\ eb 4.d}$
$\textsf{If $v_x=-9.80$ units and $v_y=-6.40$ units,}\\$
$\textit{determine the magnitude and direction of $V$.}$
\begin{align*}\displaystyle
magnitude&=\sqrt{(-9.8)^2+(-6.4)^2}
=\color{red}{11.7047}\\
direction&=\arctan{\left[\frac{6.4}{-9.8}\right]}
=\color{red}{33.15^o}
\end{align*}

ok the direction is actually in the Q4 but $\arctan{\left[\frac{-6.4}{-9.8}\right]}$
is in Q1! Do we just add $180^o$ for that or is it $-33.15^o$

The direction would be in quadrant III, and so recognizing that both components are negative, you would in fact add $\pi$ to the angle:

$$\theta=\pi+\arctan\left(\frac{v_y}{v_x}\right)$$

karush said:
Also is there symbols for magnitude and direction other than an arrow on the graph

Also where is the latex for degree instead of ^o

I use ^{\circ} for the degree symbol.
 
MarkFL said:
The direction would be in quadrant III, and so recognizing that both components are negative, you would in fact add $\pi$ to the angle:

$$\theta=\pi+\arctan\left(\frac{v_y}{v_x}\right)$$

$\textsf{ok so it}$ $$33.15^\circ + 180^\circ = 213.15^\circ $$
that would place it Q3

MarkFL said:
I use ^{\circ} for the degree symbol.

actually why don't we have \degree on the Symbol/Command Set:
 
It was an oversight I suppose, but adding it now would require a lot of effort. :)
 
I completely understand:cool:
 

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