Question

Determine the magnitude of the sum of vectors. please help i’m not sure what to do once i have the components.

Answer 1

110.24

Step-by-step explanation:

First, let us decompose the vectors into their components.

For the vector on the right, decomposing into components gives:

x - component: 80 cos (30°)

y - component: 80 sin (30°)

Therefore.

`v_(right)=[80\cos(30^o),80\sin(30^o)]`

Now for the vector on the left, we have

x - component: 91 cos (130°)

y - componentL 91 sin (130°)

Therefore,

`v_(left)=[91\cos(130^o),91\sin(130^o)]`

Now adding these two vectors gives

`v_(r\imaginaryI ght)+v_(left)=[80\cos(30^o),80\sin(30^o)]+[91\cos(130^o),91\sin(130^o)]`

Adding the components gives

`v_(r\imaginaryI ght)+v_(left)=[80\cos(30^o)+91\cos(130^o),80\sin(30^o)+91\sin(130^o)]`

Now since cos (30) = √3/ 2, sin 30 = 1/2, cos (130) = -.0643, and sin (130) = 0.766; the above becomes

`v_{r\mathrm{i}ght}+v_(left)=[(80√(3))/(2)+91(-0.643),80*(1/2)+91*(0.766)]`

the above simplifies to give ( using a calculator)

`v_{r\mathrm{i}ght}+v_(left)=[10.79,109.71]`

Now the final step is to find the magnitude of the above vector.

`|v_{r\mathrm{i}ght}+v_(left)|=√((10.79)^2+(109.71)^2)`
`\boxed{|v_{r\mathrm{i}ght}+v_(left)|=110.24.}`

which is our answer!