Two tugboat A and B tow alarge boat in an easterly direction the cable which are connected to A and B respectectively make angles of 45 degrees north of east and 30 degrees south of east to the direction of motion (question it the tension fa is equal to 10000N calculate the component force that Fa exert in a northerly direction 2 themagnitude of the southern component of Fb 3 the magnitude of Fb 4 the resultant force that A and B exert on the large boet in an easterly direction

To solve this problem, we can break down the forces and use trigonometry to find the components. Let's proceed step by step.

1. Calculate the component force that Fa exerts in a northerly direction:
The angle between the force Fa and the north direction is 45 degrees. So, we can use cosine:

Fa_north = Fa * cos(angle)
Fa_north = 10000N * cos(45°)
Fa_north ≈ 7071.07N

Therefore, the component force that Fa exerts in a northerly direction is approximately 7071.07N.

2. Calculate the magnitude of the southern component of Fb:
The angle between the force Fb and the south direction is 30 degrees. So, we can use sine:

Fb_south = Fb * sin(angle)
Fb_south = Fb * sin(30°)

Unfortunately, the magnitude of Fb is not provided, so we cannot calculate the southern component of Fb without more information.

3. Calculate the magnitude of Fb:
As mentioned earlier, we require additional information to calculate the magnitude of Fb. If you provide the value of the magnitude, we can proceed with the calculation.

4. Calculate the resultant force that A and B exert on the large boat in an easterly direction:
To find the resultant force, we need to find the horizontal components of Fa and Fb:

Fa_east = Fa * sin(angle)
Fa_east = 10000N * sin(45°)
Fa_east ≈ 7071.07N

Fb_east = Fb * cos(angle)
Fb_east = Fb * cos(30°)

To find the resultant force, we can add Fa_east and Fb_east:

Resultant force = Fa_east + Fb_east

Without the magnitude of Fb, we can't calculate the resultant force accurately.

To solve this problem, we can break down the forces into their horizontal and vertical components. Let's denote the horizontal component of the force as Fx and the vertical component as Fy.

1. To calculate the component force Fa exerts in a northerly direction:
Since Fa makes an angle of 45 degrees north of east, we can use trigonometry to find Fy:
Fy = Fa * sin(45 degrees)
Fy = 10000 N * sin(45 degrees)
Fy ≈ 7071 N (rounded to nearest whole number)

2. To calculate the magnitude of the southern component of Fb:
Since Fb makes an angle of 30 degrees south of east, we can use trigonometry to find Fy:
Fy = Fb * sin(30 degrees)
Fy = Fb * (-sin(30 degrees)) (since it is south of east)
Fy = -Fb * 0.5
-Fb * 0.5 = -7071 N (Since Fy is directed south, it is negative)
Fb ≈ 14142 N (rounded to nearest whole number)

3. To calculate the magnitude of Fb:
Since we have the vertical component of Fb from the previous step, we can find the magnitude using the Pythagorean theorem:
Fb^2 = Fx^2 + Fy^2
Fb^2 = (Fb * cos(30 degrees))^2 + (-7071 N)^2 (using the given angle and Fy)
Fb^2 = (Fb * 0.866)^2 + 50000041 N^2 (using cos(30 degrees) ≈ 0.866)
0.75Fb^2 = 50000041 N^2 (simplifying the equation)
Fb^2 ≈ 66666722.67 (dividing both sides by 0.75)
Fb ≈ 8165 N (rounded to nearest whole number)

4. To calculate the resultant force that A and B exert on the large boat in an easterly direction:
The resultant force can be found by adding the horizontal components of both forces:
Fx = Fa * cos(45 degrees) + Fb * cos(30 degrees)
Fx = 10000 N * cos(45 degrees) + 8165 N * cos(30 degrees)
Fx ≈ 11242 N (rounded to nearest whole number)

Therefore,
1. The component force Fa exerts in a northerly direction is approximately 7071 N.
2. The magnitude of the southern component of Fb is approximately 14142 N.
3. The magnitude of Fb is approximately 8165 N.
4. The resultant force that A and B exert on the large boat in an easterly direction is approximately 11242 N.