Eb 4.d determine the magnitude and direction of V

In summary, to determine the magnitude and direction of $V$ given $v_x=-9.80$ units and $v_y=-6.40$ units, we can use the equations $magnitude=\sqrt{(-9.8)^2+(-6.4)^2}$ and $direction=\arctan{\left[\frac{6.4}{-9.8}\right]}$, which give us a magnitude of $11.7047$ and a direction of $33.15^\circ$. However, since the direction is in quadrant IV, we need to add $180^\circ$ to get a final direction of $213.15^\circ$. The degree symbol can be represented in LaTeX as ^{\circ
  • #1
karush
Gold Member
MHB
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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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  • #2
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:

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

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.
 
  • #3
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:

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

$\textsf{ok so it}$ \(\displaystyle 33.15^\circ + 180^\circ = 213.15^\circ \)
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:
 
  • #4
It was an oversight I suppose, but adding it now would require a lot of effort. :)
 
  • #5
I completely understand:cool:
 

FAQ: Eb 4.d determine the magnitude and direction of V

What is "Eb 4.d" in the context of determining the magnitude and direction of V?

"Eb 4.d" refers to a specific step or requirement in a scientific process or formula that is used to determine the magnitude and direction of V. It could be a specific calculation, measurement, or procedure that is necessary to complete in order to accurately determine the magnitude and direction of V.

How do you determine the magnitude of V?

The magnitude of V can be determined by using the Pythagorean theorem, which states that the magnitude of a vector can be found by taking the square root of the sum of the squares of its components. In this case, the components would be the x and y values of V.

How do you determine the direction of V?

The direction of V can be determined by using trigonometric functions, such as tangent or sine. These functions can be used to find the angle between V and a known reference direction, such as the x-axis.

What units are typically used to measure the magnitude of V?

The magnitude of V is typically measured in units of length, such as meters or kilometers. This is because V represents a physical quantity, such as velocity or displacement, which are commonly measured in units of length.

Are there any special considerations when determining the magnitude and direction of V in a three-dimensional space?

Yes, when working in a three-dimensional space, the magnitude and direction of V can be determined using a similar process as in two-dimensional space. However, the calculation may involve an additional component, such as the z-axis, and the use of more complex trigonometric functions. Additionally, the units for magnitude may change depending on the specific application.

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