The resultant of the four forces on the balloon is 1,212.35 N at 62⁰.
The given parameters;
Force applied to the north = 5120 NForce applied to the west = 1520 NForce applied to the east = 950 NForce applied to the south = 4050 NThe resultant vertical force is calculated as follows;
[tex]F_y = 5120 \ N - 4050 \ N\\\\F_y = 1,070 \ N[/tex]
The resultant horizontal force is calculated as follows;
[tex]F_x = 1520 \ N - \ 950 \ N\\\\F_x = 570 \ N[/tex]
The resultant of the four forces is calculated as follows;
[tex]F = \sqrt{F_y^2 + F_x^2} \\\\F = \sqrt{(1,070)^2 + (570)^2} \\\\F = 1,212.35 \ N[/tex]
The direction of the force is calculated as follows;
[tex]\theta = tan^{-1} (\frac{1070}{570} )\\\\\theta = 62^0[/tex]
Thus, the resultant of the four forces on the balloon is 1,212.35 N at 62⁰.
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