Eb 4.d determine the magnitude and direction of V

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Discussion Overview

The discussion revolves around determining the magnitude and direction of a vector \( V \) given its components \( v_x = -9.80 \) units and \( v_y = -6.40 \) units. Participants explore the calculation of both the magnitude and the angle, including considerations of the vector's quadrant and the appropriate use of mathematical notation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the magnitude as \( 11.7047 \) and initially finds the direction as \( 33.15^\circ \) using \( \arctan{\left[\frac{6.4}{-9.8}\right]} \).
  • Another participant points out that the direction is actually in quadrant III, suggesting that \( 180^\circ \) should be added to the angle, resulting in \( 213.15^\circ \).
  • There is a discussion about the correct representation of angles in LaTeX, with one participant suggesting the use of \( ^{\circ} \) for the degree symbol.
  • Participants express uncertainty about the appropriate notation for magnitude and direction on graphs.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct angle for the direction of vector \( V \), as there are differing views on how to interpret the quadrant and the angle calculation. The discussion remains unresolved regarding the best approach to represent the angle and the notation for degrees.

Contextual Notes

There are unresolved questions about the notation for degrees in LaTeX and the representation of magnitude and direction on graphs. The discussion reflects a mix of mathematical reasoning and notation preferences.

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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