Two people pull a mule. One with 120 Newtons and an angle of 60 degrees. The other with 80 N and an angle of 105 degrees (Q2). What would be the force a third person would have to exert on the mule to make the net force equal to zero.

Answer 1

Do a vector addition that says that the sum of the first two forces and the unknown third force is zero. You will end up with equations for the x and y components of the unknown frce

Answer 2

120[60] + 80[105] + F3 = 0.
39.3 + 181.2i + F3 = 0.
F3 = -39.3 - 181.2i(Q3).

Tan A = (-181.20/(-39.3) = 4.61069.
A = 77.8o S. of W. = 257.8o CCW.

F3 = (-181.2)/sin257.8 = 185.4N.[257.8].

Answer 3

Or
F1 + F2 = 39.3 + 181.2i = 185.4N.[77.8o]

F3 = F1+F2, But 180o out of phase:

F3 = 185.4[77.8+180) = 185.4N.[257.8].