1. Find the resultant due to the action of three forces if they are F1, 100 N, 60º above the x axis; F2, 200 N, 140º above the x axis; and F3, 250 N, 320º above the x axis.

R = 103.7 N, 31.6° above x-axis

Explanation:

First we find the x components of all the forces:

F1x = F1 Cos 60°

F1x = (100 N)(Cos 60°)

F1x = 50 N

F2x = F2 Cos 140°

F2x = (200 N)(Cos 140°)

F2x = -153.2 N

F3x = F3 Cos 320°

F3x = (250 N)(Cos 320°)

F3x = 191.5 N

So, the x component of resultant will be the sum of the x component of each force:

Rx = F1x + F2x + F3x

Rx = 50 N - 153.2 N + 191.5 N

Rx = 88.3 N

Now we find the y components of all the forces:

F1y = F1 Sin 60°

F1y = (100 N)(Sin 60°)

F1y = 86.6 N

F2y = F2 Sin 140°

F2y = (200 N)(Sin 140°)

F2y = 128.5 N

F3y = F3 Sin 320°

F3y = (250 N)(Sin 320°)

F3y = -160.7 N

So, the y component of resultant will be the sum of the y component of each force:

Ry = F1y + F2y + F3y

Ry = 86.6 N + 128.5 N - 160.7 N

Ry = 54.4 N

Hence, the magnitude of resultant force will be:

|R| = √(Rx² + Ry²)

|R| = √[(88.3 N)² + (54.4 N)²]

|R| = √10756.25 N²

|R| = 103.7 N

And the direction θ will be:

θ = tan⁻¹(Ry/Rx)

θ = tan⁻¹(54.4/88.3)

θ = 31.6° above x-axis

Hence, the resultant vector will be:

R = 103.7 N, 31.6° above x-axis

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.

the area between the graph and the t axis