Question

Two forces of magnitudes 16 and 20 pounds are acting on an object. The bearings of the forces are N75E and S20E (that is, 75∘ east of north and 20∘ east of south), respectively. How many degrees east of south is the resultant force? (Round to two decimal places and do not enter the ∘ symbol.)

Answer 1

20.58

Explanation:

Force A = 16 pounds

direction = N75E = 75° in the first quadrant

Force B = 20 pounds

direction = S20E = 180° - 20° = 160° in the fourth quadrants

we resolve the forces into their x and y resultant forces.

For the y axis forces,

-(16 x sin 75°) + (20 x sin 160°) = Fy

-15.45 + 6.84 = Fy

Fy = -8.61 N

For the x axis forces'

(16 x cos 75°) + (20 x cos 160°) = Fx

-4.14 - 18.79 = Fx

Fx = -22.93 N

Resultant force =
`\sqrt{(Fx)^(2) + (Fy)^(2) }` =
`\sqrt{(-8.61)^(2) + (-22.93)^(2) }`

Resultant force = 24.49 N

angle made by the resultant force is,

∅ =
`tan^(-1)`
`(Fy)/(Fx)}`

∅ =
`tan^(-1)`
`(-8.61)/(-22.93)}`

∅ =
`tan^(-1)` 0.3755

∅ = 20.58