Look at the following picture. What would be the resultant vector of A+B? vector b is 4.78m 67 degress vector a 21 degrees 11.3mthe picture wont upload

Accepted Solution

Answer:The resultant vector, A+B, has a Magnitude of 15.02 meters and an angle of 34.23 degreesStep-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]