Question

Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

a) |w| = 9.4; θ = 72.9°
b) |w| = 9.4; θ = 107.1°
c) |w| = 14.2; θ = 72.9°
d) |w| = 14.2; θ = 107.1°

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Here, the direction angle is 107.1° and the magnitude is 14.2. Therefore, option D is the correct answer.

Given that, |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°.

We need to find magnitude and direction angle of w.

We have, w = u + v, θ=45° and ϕ=150°.

$u_{x}$=|u|cosθ=10cos45°=7.071

$u_{y}$=|u|sinϕ=$u_{y}$=|10sin45°=7.071

$v_{x}$=|v|cosθ=13cos150°=-11.25833

$v_{y}$=|v|sinϕ=$v_{y}$=13sin150°=6.5

Using this information, we get

$R_{x} =u_{x} +v_{x}$=7.071-11.25833=-4.18733

$R_{y} =u_{y} +v_{y}$=7.071+6.5=13.571

Direction angle=$tan^{-1}$(Ry/Rx)

Direction angle=$tan^{-1}$(13.571/-4.18733)

=-72.8239 or 107.1476≈107.1

Now, $|w|=\sqrt{(|u|cos \theta +|v|cos \phi )^{2}+(|u|sin \theta +|v|sin \phi )^{2}}$

=$|w|=\sqrt{(10cos45\textdegree +13cos150\textdegree )^{2}+(10sin 45\textdegree+13sin150\textdegree)^{2}}=14.2026$

Here, the direction angle is 107.1° and the magnitude is 14.2. Therefore, option D is the correct answer.

To learn more about  the magnitude and direction angle visit:

https://brainly.com/question/12977024.

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