Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X-axis of the resultant of $- - \to O A, - - \to B C$ and $- - \to D E .$

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Solution

$Y_{n e t} = α 5 cos 60 + 2 sin 30 - 1$
$= α 5 (\frac{1}{2}) + 2 \times \frac{1}{2} - 1$
$Y_{n e t} = 0.75$
$X_{n e t} = 2 cos 30 - α 5 cos 60$
$= 2 \frac{\sqrt{3}}{2} - 1.5 \times \frac{1}{2}$
$= 0.96$
$M a g = \sqrt{{(.96)}^{2} + {(0.75)}^{2}} = 1.21$
$θ = {tan}^{- 1} (\frac{.75}{.96}) = {37.99}^{o}$

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Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X-axis of the resultant of −−→OA,−−→BC and −−→DE.

Ynet=α5cos60+2sin30−1=α5(12)+2×12−1Ynet=0.75Xnet=2cos30−α5cos60=2√32−1.5×12=0.96Mag=√(.96)2+(0.75)2=1.21θ=tan−1(.75.96)=37.99o

Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X-axis of the resultant of $- - \to O A, - - \to B C$ and $- - \to D E .$