Question

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.
DATA: α= 47.5^o β= 60.8^o |A| = 5.7 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the y-component of vector B.

find y-component of B

find x-component of (A-B)

find magnitude of A+B

Answer 1

Given |A|=5,7cm,  

Firstly, the diagram of the problem is-

Now, since A-B is parallel to -x axis, hence (A-B)_y=0B_y=A_y

Now, we know |B|, and hence, we can find every part now-

B_y=|B|sin60.8^o=4.202cm

|A-B|_x=A_x-B_x= -5.7cos47.5^o-(-4.81cos60.8^o)=-1.5cm

|A+B|_x=A_x+B_x=-5.7cos47.5^o-4.81cos60.8^o=-6.20cm

|A+B|_y=A_y+B_y=5.7sin47.5^o+4.81sin60.8^o=8.40cm

Hence,