Question

(50pts) WAYYYYY overdue science assignment, NEED help with force vectors ASAP!

Answer 1

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  | = $\sqrt{x^{2}+y^{2} }$

                                  = $\sqrt{36^{2}+44^{2} }$

                                  = 56.85 N

angle = $tan^{-1} (\frac{y}{x} )$

         = $tan^{-1\frac{44}{36} }$

         = 50.71 °