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seraphim [82]
3 years ago
6

Given the vectors A⃗ and B⃗ shown in the figure ((Figure 1) ), determine the magnitude of B⃗ −A⃗. A is 28 degrees above the posi

tive x-axis and is 44m long, and B is 56 degrees above the negative x-axis and is 26.5m long

Mathematics
2 answers:
Alex_Xolod [135]3 years ago
8 0
To answer this problem, we are given with two vectors. We translate these into angle form such that the mode complex in the calculator fits in the computation. We input 44<28 + 26.5< (180-56). The answer from the calculator is 48.93< 60.59. The magnitude is 48.93 pointing to the direction of 60.59 degrees above the x axis.
Vlad [161]3 years ago
7 0

This problem is represented in the Figure below. So, we can find the components of each vector as follows:


\bullet \ cos(28^{\circ})=\frac{Adjacent}{Hypotenuse}=\frac{A_{x}}{44} \\ \\ \therefore A_{x}=44cos(28^{\circ})=38.85m \\ \\ \\ \bullet \ sin(28^{\circ})=\frac{Opposite}{Hypotenuse}=\frac{A_{y}}{44} \\ \\ \therefore A_{y}=44sin(28^{\circ})=20.65m


\bullet \ cos(56^{\circ})=\frac{Adjacent}{Hypotenuse}=\frac{-B_{x}}{26.5} \\ \\ \therefore B_{x}=-26.5cos(56^{\circ})=-14.81m \\ \\ \\ \bullet \ sin(56^{\circ})=\frac{Opposite}{Hypotenuse}=\frac{B_{y}}{26.5} \\ \\ \therefore B_{y}=26.5sin(56^{\circ})=21.97m


Therefore:

\vec{A}=(38.85, 20.65)m \\ \\ \vec{B}=(-14.81, 21.97)m


So:

\vec{B}-\vec{A}=(-14.81, 21.97)-(38.85, 20.65)=(-53.66,1.32)


Finally, the magnitude is:


\boxed{\left| \vec{B}-\vec{A}\right|=\sqrt{(-53.66)^2+(1.32)^2}=53.67m}

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