Answer:
Example A : 2.83 i + 3.94 j
Example B : -35.7 i + 6.5 j
Example C : 56.85 N, 50.71 °
Step-by-step explanation:
since all vectors are given in terms of magnitude and angle polar coordinates are the obvious choice.
A vector r with magnitude r and angle θ can be represented in polar coordinates as
r = rcosθ i + rsinθ j
where i and j are unit vectors in x , y direction
let's look at the question now ,
Example A
two vectors are given lets call the a and b
a = 23 cos27° i + 23 sin27° j = 20.5 i + 10.4j
b = 30 cos75° i + 30sin75° j = 7.8 i + 29.0 j
resultant vector,a + b =( 20.5 + 7.8 )i + (10.4 + 29.0)j
= 28.3 i + 39.4 j
if we give the scale 10 N = 1 cm vector will become
r = 2.83 i + 3.94 j
Example B
two vectors are given lets call the a and b
a = 27 cos224° i + 27 sin224° j = -19.4 i + -18.7j
b = 30 cos123° i + 30sin123° j = -16.3 i + 25.2 j
resultant vector,a + b =( -19.4 + -16.3 )i + (-18.7 + 25.2)j
=-35.7 i + 6.5 j
Example C
two vectors are given lets call the a and b
a = 16 cos80° i + 16sin80° j = 2.8 i + 15.8j
b = 48 cos144° i + 48sin144° j = -38.8 i + 28.2 j
resultant vector, a + b =( 2.8 + -38.8)i + (15.8 + 28.2)j
= 36.0 i + 44.0 j
magnitude, | a + b | = [tex]\sqrt{x^{2}+y^{2} }[/tex]
= [tex]\sqrt{36^{2}+44^{2} }[/tex]
= 56.85 N
angle = [tex]tan^{-1} (\frac{y}{x} )[/tex]
= [tex]tan^{-1\frac{44}{36} }[/tex]
= 50.71 °
