Vector G is 40.3 m long in a-35.0° direction. Vector His63.3 m long in a 270° direction.Find the magnitude of theirvector sum.magnitude (m)Enter

Accepted Solution

Answer:Approximately 92.51.Not sure what the desired rounding is since it isn't listed. Step-by-step explanation:So the first vector G is 40.3 m long in a -35 degree direction.Lat's find the components of G.[tex]G_x=40.3\cos(-35)=33.0118[/tex].[tex]G_y=40.3\sin(-35)=-23.1151[/tex].The second vector H is 63.3 m long in a 270 degree direction.[tex]H_x=63.3\cos(270)=0[/tex].[tex]H_y=63.3\sin(270)=-63.3[/tex].The resultant vector can be found by adding the corresponding components:[tex]R_x=G_x+H_x=33.0118+0=33.0118[/tex][tex]R_y=G_y+H_y=-23.1151+(-63.3)=-86.4151[/tex]Now we are asked to find the magnitude of [tex](R_x,R_y)[/tex] which is given by the formula [tex]\sqrt{R_x^2+R_y^2}[/tex].Since [tex](R_x,R_y)=(33.0118,-86.4151)[/tex] then the magnitude is [tex]\sqrt{(33.0118)^2+(-86.4151)^2}=\sqrt{8557.34844}=92.51[/tex].