A force of 10N act on a object making 30 degree angle north of east and another force of 20N act on it along north. Calculate resultant force and it's direction ?

take the 10 N and break it into components. force=10cos30 N + 10sin30E

add that to the other force
(20+10cos30)N + 10sin30E

that is the resultant.
magnitude= sqrt (N^2+E^2)
direction= arctan E/N where E, N are the components.

To calculate the resultant force, we need to use vector addition. We will first break down each force into its horizontal and vertical components. Then, we will add the horizontal components together and the vertical components together to get the resultant force.

Let's start with the force of 10 N making a 30 degree angle north of east. To find the horizontal and vertical components, we will use trigonometry.

Horizontal component = 10 N * cos(30°)
Vertical component = 10 N * sin(30°)

Now, let's calculate these components:
Horizontal component = 10 N * cos(30°) ≈ 8.66 N (rounded to two decimal places)
Vertical component = 10 N * sin(30°) = 5 N

Next, we consider the force of 20 N acting along the north direction. Since this force is only acting vertically, its vertical component is 20 N, and its horizontal component is 0 N.

Now, let's add the horizontal and vertical components together separately:

Horizontal component = 8.66 N + 0 N = 8.66 N
Vertical component = 5 N + 20 N = 25 N

Using the Pythagorean theorem, we can find the magnitude of the resultant force:

Resultant force = √(Horizontal component^2 + Vertical component^2)
Resultant force = √((8.66 N)^2 + (25 N)^2)
Resultant force ≈ √(74.9956 N^2 + 625 N^2)
Resultant force ≈ √(699.9956 N^2)
Resultant force ≈ 26.46 N (rounded to two decimal places)

To find the direction of the resultant force, we need to use trigonometry again. We can use the arctangent function to find the angle between the resultant force and the positive x-axis:

Angle = arctan(Vertical component / Horizontal component)
Angle = arctan(25 N / 8.66 N)
Angle ≈ arctan(2.89)
Angle ≈ 70.19° (rounded to two decimal places)

So, the resultant force is approximately 26.46 N, and its direction is about 70.19 degrees north of the east direction.