Question

if vector u has lenght 70 and direction 40 degrees, and vector v has length 85 and direction 335 degrees what is the length and direction of vector u plus vector v

Answer 1

Magnitude of resultant = 131.15

Direction of resultant = 3.97°

Step-by-step explanation:

||u|| = 70

θ = 40°

`\vec{u}_x=||u||cos\theta \\\Rightarrow \vec{u}_x=70cos40=53.62`

`\vec{u}_y=||u||sin\theta \\\Rightarrow \vec{u}_y=70sin40=44.99`

||v|| = 85

θ = 335°

`\vec{v}_x=||v||cos\theta \\\Rightarrow \vec{v}_x=85cos335=77.03`

`\vec{v}_y=||v||sin\theta \\\Rightarrow \vec{v}_y=85sin335=-35.92`

Resultant

`R=√(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 =√((70cos40+85cos335)^2+(70sin40+85sin335)^2)\\\Rightarrow R =131.15`

`\theta=tan^(-1)(R_y)/(R_x)\\\Rightarrow \theta=tan^(-1)(70sin40+85sin335)/(70cos40+85cos335)\\\Rightarrow \theta=tan^(-1)0.069=3.97^(\circ)`

Magnitude of resultant = 131.15

Direction of resultant = 3.97°