Find the sum of the given vectors 50N∠320∘+170N∠150∘ Rx=? Ry=? R=? θ=?

Step 1Assume that the vectors are A and B. Draw the vectors as symbols on the graph.a→=50N∠320∘b→=170N∠150∘Step 2Now, resolve the vectors a and b to get&nbsp;Rx&nbsp;and&nbsp;Ry.|a→x|=−50cos⁡50∘|a→y|=50sin⁡50∘|b→x|=170cos⁡60∘|b→y|=−170sin⁡60∘Rx=|a→x|+|b→x|Rx=−50cos⁡50∘+170cos⁡60∘Rx=52.86Ry=|a→y|+|b→y|Ry=50sin⁡50∘−170sin⁡60∘Ry=−108.92Step 3Finally, determine the resultant vector R and the direction theta using the resultant vectors&nbsp;Rx&nbsp;and&nbsp;Ry.R=Rx2+Ry2=(52.86)2+(−108.92)2=14657.746=121.07Hence,&nbsp;R=121.07θ=tan−1(RyRx)=tan−1(−180.9552.86)=−64.11∘=295.89∘≈296∘Hence, theta&nbsp;=296∘&nbsp;from horizontal axis.

Resolved: "Find the sum of the given vectors 50N∠320∘+170N∠150∘..."

iohanetc

Answered question

2020-10-25

Find the sum of the given vectors

50 N ∠ 320^{\circ} + 170 N ∠ 150^{\circ}

R x = ?

R y = ?

R = ?

θ = ?

Answer & Explanation

Luvottoq

Skilled2020-10-26Added 95 answers

Step 1
Assume that the vectors are A and B. Draw the vectors as symbols on the graph.
$\vec{a} = 50 N ∠ 320^{\circ}$
$\vec{b} = 170 N ∠ 150^{\circ}$

Step 2
Now, resolve the vectors a and b to get $R_{x} and R_{y} .$

$| {\vec{a}}_{x} | = - 50 \cos 50^{\circ}$
$| {\vec{a}}_{y} | = 50 \sin 50^{\circ}$
$| {\vec{b}}_{x} | = 170 \cos 60^{\circ}$
$| {\vec{b}}_{y} | = - 170 \sin 60^{\circ}$
$R_{x} = | {\vec{a}}_{x} | + | {\vec{b}}_{x} |$
$R_{x} = - 50 \cos 50^{\circ} + 170 \cos 60^{\circ}$
$R_{x} = 52.86$
$R_{y} = | {\vec{a}}_{y} | + | {\vec{b}}_{y} |$
$R_{y} = 50 \sin 50^{\circ} - 170 \sin 60^{\circ}$
$R_{y} = - 108.92$
Step 3
Finally, determine the resultant vector R and the direction theta using the resultant vectors $R_{x} and R_{y} .$
$R = \sqrt{R_{x}^{2} + R_{y}^{2}}$
$= \sqrt{{(52.86)}^{2} + {(- 108.92)}^{2}}$
$= \sqrt{14657.746}$
$= 121.07$
Hence, $R = 121.07$
$θ = \tan^{- 1} (\frac{R_{y}}{R_{x}})$
$= \tan^{- 1} (\frac{- 180.95}{52.86})$
$= - {64.11}^{\circ}$
$= {295.89}^{\circ}$
$\approx 296^{\circ}$
Hence, theta $= 296^{\circ}$ from horizontal axis.

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