Question

. The following force vectors act on an object: i) 55.0 newtons at 45.0° north of east and ii) 20.0 newtons at 30.0° south of east. Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?

Answer 1

`F = 62.93`

`\theta = 27.20^0`

Step-by-step explanation:

Let us assume

east as positive

calculating the x components of each force:

F₁= 55 cos(45⁰)

= 38.89 N

F₂= 20 cos (30)

= 17.32 N

Y-components: (North is defined as positive)

F₁= 55 sin(45⁰)

= 38.89 N

F₂= -20 sin (30)

= -10 N

resultant force in x-direction = 38.89 + 17.32

= 56.21 N

resultant force in x-direction = 38.89 - 10

= 28.89 N

magnitude

`F = √(56.21^2+28.89^2)`

`F = 62.93`

`tan \theta = (y)/(x)`

`tan \theta = (28.89)/(56.21)`

`\theta = 27.20^0`