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

Answer:

$F = 62.93$

$\theta = 27.20^0$

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

$F = \sqrt{56.21^2+28.89^2}$

$F = 62.93$

$tan \theta = \dfrac{y}{x}$

$tan \theta = \dfrac{28.89}{56.21}$

$\theta = 27.20^0$