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

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.

layers of the earth affect the waves and these effects are seen on instruiments such as seimometers

close lines strong magnet less close weaker