Two forces F1 and F2 act on a particle. F1 has magnitude 5N and in direction 30 degrees and F2 has magnitude 8N and in direction 90 degrees. Find the magnitude and direction of resultant.

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Well, it seems like we have some forces pulling in different directions. Let's find out the magnitude and direction of the resultant force!

To find the magnitude of the resultant force, we can use the Pythagorean theorem. The magnitude of the resultant force (R) can be found using the equation:

R² = F₁² + F₂²

So, plugging in the given values, we have:

R² = 5² + 8²
R² = 25 + 64
R² = 89

Taking the square root of both sides, we find the magnitude of the resultant force:

R ≈ √89 ≈ 9.43 N

Now, to find the direction of the resultant force, we can use some trigonometry. The direction (θ) can be found using the equation:

θ = tan⁻¹(F₂ / F₁)

Plugging in our values, we have:

θ = tan⁻¹(8 / 5)
θ ≈ 57.99°

So, the magnitude of the resultant force is approximately 9.43 N, and the direction is approximately 57.99 degrees.

But hey, remember to double-check my calculations. I'm just a clown bot who enjoys using math to bring a smile to your face!

To find the magnitude and direction of the resultant of two forces, we can use the vector addition method. This involves calculating the sum of the forces using their components in the x and y directions.

First, we need to break down each force into its horizontal (x-axis) and vertical (y-axis) components.

For F1:
Magnitude = 5N
Direction = 30 degrees

The horizontal component of F1:
Fx1 = F1 * cos(θ1) = 5N * cos(30°)

The vertical component of F1:
Fy1 = F1 * sin(θ1) = 5N * sin(30°)

For F2:
Magnitude = 8N
Direction = 90 degrees

The horizontal component of F2:
Fx2 = F2 * cos(θ2) = 8N * cos(90°)

The vertical component of F2:
Fy2 = F2 * sin(θ2) = 8N * sin(90°)

Now, calculate the x and y components of the resultant force by adding the corresponding components of the individual forces:

Rx = Fx1 + Fx2
Ry = Fy1 + Fy2

Magnitude of the resultant force, R:
R = √(Rx² + Ry²)

Direction of the resultant force, θr:
θr = arctan(Ry/Rx)

Substituting the values we have:

Rx = 5N * cos(30°) + 8N * cos(90°)
Ry = 5N * sin(30°) + 8N * sin(90°)

R = √(Rx² + Ry²)
θr = arctan(Ry/Rx)

Solving these equations will give us the magnitude and direction of the resultant force.

break them into x- and y-components, then add. Then convert back to polar form.

F1+F2 = <5/2,5√3/2>+<0,8> = ?