Respuesta :
Answer:
The magnitude of A is 17.46 m and B is 1.50 m
Step-by-step explanation:
If the vector sum A+B+C =0, then the sum of the projection of the vector in axes x- is zero and the sum of the projection of the vector in the axes y- is also zero.
Ax+Bx+Cx = 0
Ay+By+Cy = 0
|Ax| = cos 41.9 * |A|
|Ay| = sin 41.9 * |A|
|Bx| = cos 28.2 * |B|
|By| = sin 28.2 * |B|
|Cx| = 0
|Cy| = 22.2
Ax+Bx+Cx = 0
|Ax|-|Bx|+0 =0
the vector Ax is in the positive direction of the x- axes and Bx in the negative direction and C do not have a component in the x- axes
cos 41.9 * |A| - cos 28.2 * |B| = 0 (I)
Ay+By+Cy = 0
|Ay|+|By|-|Cy|=0
the vector Ay and By are the positive direction of the y- axes and Cy in the negative direction
sin 41.9 * |A| + sin 28.2 * |B| - 22 =0 (II)
Now we have a system of 2 (I and II) equations and 2 variables (|A| and |B|)
cos 41.9 * |A| - cos 28.2 * |B| = 0
sin 41.9 * |A| + sin 28.2 * |B| = 22
cos 41.9 * |A| = cos 28.2 * |B|
|A| = cos 28.2 * |B| / cos 41.9
sin 41.9 * |A| + sin 28.2 * |B| = 22
sin 41.9 * cos 28.2 * |B| / cos 41.9 + sin 28.2 * |B| = 22
tg 41.9 * cos 28.2 * |B| + sin 28.2 * |B| = 22
(tg 41.9 * cos 28.2 + sin 28.2) * |B| = 22
|B| = 22 / (tg 41.9 * cos 28.2 + sin 28.2)
|B| = 17.46
|A| = 1.50
The magnitude of vector A and the magnitude of vector B is 20.6198 and 17.4146 respectively.
What is a vector?
The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
Given
Vector C has a magnitude of 22.2 m and points in the negative y‑direction.
Vectors A and B both have positive y‑components and make angles of α=41.9° and β=28.2° with the positive and negative x-axis.
Let the vectors A, B, and C be concurrent.
Then vectors can be resolved in x-direction and y-direction.
Vectors in y-direction
[tex]\rm A\ sin 41.9^o + B \ sin28.2^o = C\\0.6678\ A\ \ +\ 0.4726\ B \ = 22[/tex].....eq(1)
Vectors in x-direction
[tex]\rm A \ cos41.9^o = B \ cos 28.2^o\\0.74431 \ \ A = B \ \ 0.8813[/tex].....eq(2)
From equations 1 and 2, we get
A = 20.6199 and B = 17.4147
Thus, the magnitude of vector A and the magnitude of vector B is 20.6198 and 17.4146 respectively.
More about the vector link is given below.
https://brainly.com/question/13188123
