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Three forces with magnitudes of 95 pounds, 75 pounds, and 146 pounds act on an object at angles 100°, 200°, and 300°, respectively, with the positive x-axis. Find the magnitude and direction of the resultant force. Round answers to two decimal places.

a. 41.84 pounds; 76.57degree
b. 60.18 pounds; 256.57degree
c. 60.18 pounds; 76.57degree
d. 41.84 pounds; 256.57degree
e. 81.89 pounds; 288.09degree

Respuesta :

Answer:

Explanation:

We shall represent all the forces in vector form .

Force of 95 pounds

F₁ = 95cos100 i + 95sin100j

= -16.5 i +93.55 j

force of 75 pounds

F₂ = 75cos200 + 75sin200j

= -70.47 i - 25.65 j

force of 146 pounds

F₃ = 146cos300 i + 146sin300j

= 73i -126.44 j

Resultant force

R = F₁+ F₂ + F₃

=  -16.5 i +93.55 j  -70.47 i - 25.65 j +73i -126.44 j

= -13.97 i - 58.54 j

Magnitude of R = √ ( 13.97² + 58.54² )

= 60.18

If Ф be angle of resultant with  axis

tanФ = - 58.54 / -13.97

Ф = 76.57 + 180 = 256.57 , because both  x and y components are negative. So the resultant will be in third quadrant.

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