forces of 20N to the south,40N to the northeast, and 10N to be east act on the object.the magnitude of resultant force is

a)10N b)39 N
c)20 N d)46 N

Force=39N

Well, well, well, looks like someone's trying to test my physics knowledge! Let me put on my thinking cap for a moment.

Alright, so we have three forces acting on the object. Now, if you're looking for the magnitude of the resultant force, we need to use some fancy vector math. Don't worry, I'll keep it simple!

Let's break down each force into its northward and eastward components.

The 20N force to the south doesn't have any eastward component, so we can ignore that.

The 10N force to the east doesn't have any northward component, so we can ignore that too.

But the 40N force to the northeast, well, that's the tricky part! We need to find its northward and eastward components.

Using some basic trigonometry, we can find that the northward component is 40N * sin(45) = 28.28N, and the eastward component is 40N * cos(45) = 28.28N as well.

Now, let's add up all the northward and eastward components separately.

Northward component: 28.28N + 0N = 28.28N
Eastward component: 28.28N + 28.28N = 56.56N

To find the magnitude of the resultant force, we'll use the good old Pythagorean theorem! The magnitude would be the square root of (28.28N squared + 56.56N squared), which simplifies to approximately 63.25N.

So, none of the options provided match our calculated magnitude. Looks like we need to go back to the drawing board and find a better option! Keep on trying, my friend!

To determine the magnitude of the resultant force, we need to find the vector sum of the given forces.

We can break down each force into its x-component and y-component:

Force 1: 20N to the south
x-component: 0N
y-component: -20N

Force 2: 40N to the northeast
To calculate the x-component and y-component, we use the fact that the northeast direction is halfway between north and east.

x-component: cos(45) * 40N = 28.28N (approximately)
y-component: sin(45) * 40N = 28.28N (approximately)

Force 3: 10N to the east
x-component: 10N
y-component: 0N

Now, we can add up the x-components and y-components separately:

Total x-component: 0N + 28.28N + 10N = 38.28N (approximately)
Total y-component: -20N + 28.28N + 0N = 8.28N (approximately)

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

Resultant force = sqrt((Total x-component)^2 + (Total y-component)^2)
Resultant force = sqrt((38.28N)^2 + (8.28N)^2)
Resultant force = sqrt(1468.78N^2 + 68.38N^2)
Resultant force = sqrt(1537.16N^2)
Resultant force = 39.19N (approximately)

Therefore, the magnitude of the resultant force is approximately 39N.
The correct answer is b) 39N.

To find the magnitude of the resultant force, we need to combine the individual forces acting on the object.

We can start by breaking down the forces into their horizontal and vertical components.

The force of 20N to the south is only acting in the vertical (downward) direction, so its vertical component is 20N and its horizontal component is 0N.

The force of 40N to the northeast can be split into its horizontal and vertical components using trigonometry. The angle between this force and the horizontal axis is 45 degrees because it is aiming northeast. The horizontal component is given by 40N * cos(45°) = 40N * (sqrt(2)/2) ≈ 28.284N. The vertical component is given by 40N * sin(45°) = 40N * (sqrt(2)/2) ≈ 28.284N.

The force of 10N to the east is only acting in the horizontal direction, so its horizontal component is 10N and its vertical component is 0N.

Now, we can add the horizontal components and vertical components separately to find the total horizontal and vertical forces.

Horizontal force = 0N + 28.284N + 10N = 38.284N
Vertical force = -20N + 28.284N + 0N = 8.284N

To find the magnitude of the resultant force, we can use the Pythagorean theorem:
Resultant force = sqrt((Horizontal force)^2 + (Vertical force)^2)
= sqrt((38.284N)^2 + (8.284N)^2)
≈ sqrt(1464.205856 + 68.544656)
≈ sqrt(1532.750512)
≈ 39.14N

Therefore, the magnitude of the resultant force is approximately 39N, so the correct answer is b) 39N.

Fr = 20N[270o] + 40N[45o] + 10[0o] =

-20i + 40*cs45) + i40*sin45) + 10 =
-20i + 28.28 + 28.28i + 10=38.28 + 8.28i

Fr^2 = 38.28^2 + 8.28^2 = 1533.9
Fr = 39 N.