Question

Two forces act on an object. The first force has a magnitude of 360 newtons and acts at an angle of 30° as measured from the horizontal. The second force has a magnitude of 240 newtons and acts at an angle of 135° as measured from the horizontal. Determine the vector v that represents the resultant force.

Answer 1

B)
`v=(180√(3) -120√(2))i+(18 0+120√(2) )j`

Explanation:

I just did the test and this is the correct answer.

Answer 2

Answer:377.46 N

Explanation:

Given

Vector 1 has a magnitude of
`360\ N` and makes an angle of
`30^(\circ)`

vector 2 has a magnitude of
`240\ N` and makes an angle of
`135^(\circ)`

Net Horizontal force

`\sum F_h=360\cos 30+240\cos 135`

`\sum F_h=311.769-169.70`

`\sum F_h=142.069\ N\quad \ldots(i)`

Net vertical force

`\sum F_v=360\sin 30+240\sin 135`

`\sum F_v=180+169.705`

`\sum F_v=349.705\ N\quad \ldots(ii)`

Net resultant force

`F_(net)=√(F_h^2+F_v^2)`

`F_(net)=√((142.069)^2+(349.705)^2)`

`F_(net)=377.46\ N`

angle which resultant make with x-axis

`\tan \theta =(\sum F_v)/(\sum F_h)`

`\tan \theta =(349.705)/(142.069)`

`\tan \theta =2.461`

`\theta =67.88^(\circ)`

Thus vector v is given by

`\vec{v}=377.46[\cos 67.88+\sin 67.88]`