Answer:
The resultant vector, A+B, has a Magnitude of 15.02 meters and an angle of 34.23 degrees
Step-by-step explanation:
We need to convert the vectors given to x,y coordinate form.
We use the formula below:
[tex]x=ACos\theta[/tex]
[tex]y=ASin\theta[/tex]
Where A is the magnitude and [tex]\theta[/tex] is the angle.
Vector A:
[tex]x=ACos\theta\\x=(11.3)Cos(21)\\x=10.55[/tex]
and
[tex]y=(11.3)Sin(21)\\y=4.05[/tex]
Vector B:
[tex]x=(4.78)Cos(67)\\x=1.87[/tex]
and
[tex]y=(4.78)Sin(67)\\y=4.40[/tex]
Now we can write the vectors as:
A = <10.55,4.05>
B = <1.87,4.40>
To add, A+B, we have:
A + B = <10.55+1.87, 4.05+4.40>
A + B = < 12.42, 8.45 >
To convert this into magnitude/degree format:
Magnitude = [tex]\sqrt{(12.42)^2 + (8.45)^2} =15.02[/tex]
Angle = [tex]Tan^{-1}(\frac{8.45}{12.42})=34.23[/tex]
