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.

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

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].

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].

To find the force that a third person would have to exert on the mule to make the net force equal to zero, we need to consider the components of the forces applied by the two people.

First, let's find the x- and y-components of the forces:

For the first person:
- Force: 120 N
- Angle: 60 degrees
To find the x-component, we multiply the force by the cosine of the angle:
120 N * cos(60 degrees) = 60 N
To find the y-component, we multiply the force by the sine of the angle:
120 N * sin(60 degrees) = 103.92 N (approximately)

For the second person:
- Force: 80 N
- Angle: 105 degrees
To find the x-component, we multiply the force by the cosine of the angle:
80 N * cos(105 degrees) = -30.81 N (approximately) (negative because it is in the opposite direction)
To find the y-component, we multiply the force by the sine of the angle:
80 N * sin(105 degrees) = 75.63 N (approximately)

Now, let's add the x- and y-components separately to find the net force in the x-direction and the y-direction.

In the x-direction:
60 N - 30.81 N = 29.19 N (approximately)

In the y-direction:
103.92 N + 75.63 N = 179.55 N (approximately)

To make the net force equal to zero, the third person's force must cancel out the net force in both the x- and y-directions.

So, the net force in the x-direction is 29.19 N. The force from the third person in the x-direction should be -29.19 N.

The net force in the y-direction is 179.55 N. The force from the third person in the y-direction should be -179.55 N.

Therefore, the force a third person would have to exert on the mule to make the net force equal to zero would be approximately 29.19 N in the x-direction and approximately 179.55 N in the y-direction.