I got 10 right, By= -3.86 cm but I cant figure out 11. Algebra based and please

Question

I got 10 right, By= -3.86 cm but I cant figure out 11. Algebra based and please explain thoroughly. Thanks!

10. [1pt] The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated. DATA: alpha = 46.7 degrees, beta 53.8 degrees A 5.30 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the y component of vector B Correct, computer gets: -3.86E+00 cm Hint: Since the sum vector (A-B) has no y-component, vector A must have the same y-component as vector B. As shown, east is for +x, and north' for +y, thus the answer can be negative. 11. [lpt] Calculate the x component of the vector A -B

Explanation / Answer

10)

A=(Ax)i+(Ay)j

=[A*cos(alpa)]i+[A*sin(alpa)]j

=[5.3*cos(46.7)]i+[5.3*sin(46.7)]j

A=(3.63)i+(3.86)j

(Ax)i+(Ay)j=(3.63)i+(3.86)j

and

B=(Bx)i+(By)j

now

let, resultent vector R=A-B is parallel to -x-axis

and

R=A-B

(Rx)i+(Ry)j=(Ax)i+(Ay)j+(Bx)i+(By)j

(Rx)i+(0)j=(Ax+Bx)i+(Ay+By)j

Rx=Ax+Bx

and

Ry=Ay+By

0=Ay+By

By=-Ay

By=-3.86 cm ------is the y -component of vector B

11)

By=B*cos(beta)

B=By/cos(beta)

B=3.86/cos(53.8)

B=6.53 cm

and

Bx=B*sin(beta)

=6.53*sin(53.8)

=5.27 cm

now,

now,

the x-component of R=A-B is Rx=Ax+Bx

=3.63-5.27

Rx= -1.64 cm

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