Three forces with magnitudes pounds, pounds and pounds act on an object at angles respectively, with the positive x-axis.Find the direction and magnitude
Of the resultant force.(The choices below are given to two decimal places.)
A) with the positive x-axis
B) with the positive x-axis
C) with the positive x-axis
D) with the positive x-axis
E)with the positive x-axis

Question

Three forces with magnitudes  pounds,  pounds and  pounds act on an object at angles  respectively, with the positive x-axis.Find the direction and magnitude
Of the resultant force.(The choices below are given to two decimal places.)
A) with the positive x-axis 
B) with the positive x-axis 
C) with the positive x-axis 
D) with the positive x-axis 
E)with the positive x-axis

Quizplus · Accepted Answer

To find the magnitude of the resultant force, we can use the formula:
R^2 = F1^2 + F2^2 + F3^2 + 2F1F2cos(theta1-theta2) + 2F1F3cos(theta1-theta3) + 2F2F3cos(theta2-theta3)
where R is the magnitude of the resultant force, F1, F2, and F3 are the magnitudes of the three forces, and theta1, theta2, and theta3 are the angles they make with the positive x-axis. 
Substituting the given values, we get:
R^2 = (11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)^2 + (11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)^2 + (11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)^2 + 2(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)(11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11 - 11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 2(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)(11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11 - 11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11) + 2(11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)(11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)cos(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11 - 11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11)
Simplifying this expression, we get:
R^2 = 781.06
Taking the square root, we get:
R = 27.96 lbs (approx)
The direction of the resultant force can be found using the formula:
tan(theta) = (F1sin(theta1) + F2sin(theta2) + F3sin(theta3))/(F1cos(theta1) + F2cos(theta2) + F3cos(theta3))
Substituting the given values, we get:
tan(theta) = (11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11sin(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11) + 11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11sin(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11sin(11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11))/(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11) + 11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11cos(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11cos(11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11))
Simplifying this expression, we get:
tan(theta) = -0.37
Taking the inverse tangent, we get:
theta = -19.12 degrees (approx)
Since the given angles are all in the first quadrant, the direction of the resultant force will be in the fourth quadrant (i.e. negative x-axis). Therefore, the answer is E, with the positive x-axis 11ebbd4d_3efc_36ff_8a0a_73e212fa01e1_TB8202_11.

Three Forces with Magnitudes Pounds, Pounds and