Answer:
Magnitude of resultant = 131.15
Direction of resultant = 3.97°
Explanation:
||u|| = 70
θ = 40°
[tex]\vec{u}_x=||u||cos\theta \\\Rightarrow \vec{u}_x=70cos40=53.62[/tex]
[tex]\vec{u}_y=||u||sin\theta \\\Rightarrow \vec{u}_y=70sin40=44.99[/tex]
||v|| = 85
θ = 335°
[tex]\vec{v}_x=||v||cos\theta \\\Rightarrow \vec{v}_x=85cos335=77.03[/tex]
[tex]\vec{v}_y=||v||sin\theta \\\Rightarrow \vec{v}_y=85sin335=-35.92[/tex]
Resultant
[tex]R=\sqrt{R_x^2+R_y^2}\\\Rightarrow R=\sqrt{(\vec{u}_x+\vec{v}_x)^2+(\vec{u}_y+\vec{v}_y)^2}\\\Rightarrow R =\sqrt{(70cos40+85cos335)^2+(70sin40+85sin335)^2}\\\Rightarrow R =131.15[/tex]
[tex]\theta=tan^{-1}\frac{R_y}{R_x}\\\Rightarrow \theta=tan^{-1}\frac{70sin40+85sin335}{70cos40+85cos335}\\\Rightarrow \theta=tan^{-1}0.069=3.97^{\circ}[/tex]
Magnitude of resultant = 131.15
Direction of resultant = 3.97°
