An object is acted by 3 coplanar forces:30 newton to the north, 20 in the direction S20degrees E and 25 newton in a direction W20degrees S.Find the resultant

S20DegE = 290Deg CCW.

W20DegS = 200Deg CCW.

X = hor. = 25cos200 + 20cos290,
X = -23.49 + 6.84 = -16.65N.

Y = ver. = 30 + 25sin200 + 20sin290,
Y = 30 - 8.55 - 18.79 = 2.66N.

tanA = Y/X = 2.66/-16.65 = -0.1596,
A=-9.07Deg = -9.07 +180 = 170.9Deg,Q2.

R = X/cosA = -16.65 / cos170.9 = 16.9N.
@ 170.9Deg.

To find the resultant of the three forces acting on the object, we need to determine the magnitude and direction of the resultant force.

1. Start by drawing a diagram to represent the forces.
- Draw an arrow to represent each force, with each arrow pointing in the direction of the force.
- Label the arrows with the magnitudes of the forces (30 N, 20 N, and 25 N).

2. Next, find the horizontal and vertical components of each force.
- Break down each force into horizontal and vertical components using trigonometry (sine and cosine functions).
For Force A (30 N to the north):
- Vertical component: 30 N * cos(0°) = 30 N * 1 = 30 N (since it is already in the vertical/north direction)
- Horizontal component: 30 N * sin(0°) = 30 N * 0 = 0 N (since it does not have any horizontal component)

For Force B (20 N in the direction S20°E):
- Vertical component: 20 N * cos(20°) = 20 N * 0.9397 ≈ 18.79 N (positive since it is facing downwards)
- Horizontal component: 20 N * sin(20°) = 20 N * 0.3420 ≈ 6.84 N (positive since it is facing east)

For Force C (25 N in the direction W20°S):
- Vertical component: 25 N * cos(70°) = 25 N * -0.3420 ≈ -8.55 N (negative since it is facing upwards)
- Horizontal component: 25 N * sin(70°) = 25 N * -0.9397 ≈ -23.49 N (negative since it is facing west)

3. Sum up the horizontal and vertical components of each force to find the resultant components.
- Vertical component: 30 N + 18.79 N + (-8.55 N) ≈ 40.24 N (positive, as the positive direction is upwards)
- Horizontal component: 0 N + 6.84 N + (-23.49 N) ≈ -16.65 N (negative, as the positive direction is east)

4. Calculate the magnitude of the resultant.
- Magnitude: √[(vertical component)² + (horizontal component)²]
- Magnitude: √[(40.24 N)² + (-16.65 N)²] ≈ √[1619.62 N² + 277.33 N²] ≈ √1896.95 N² ≈ 43.55 N

5. Calculate the direction of the resultant.
- Direction: tan^(-1)(vertical component / horizontal component)
- Direction: tan^(-1)(40.24 N / -16.65 N) ≈ tan^(-1)(-2.416) ≈ -68.65°

Therefore, the resultant of the three forces is approximately 43.55 N in magnitude, angled at -68.65° (measured counterclockwise from the positive x-axis).