Your friend has slipped and fallen. To help her up, you pull with a force F, as the drawing shows. The vertical component of this force is 140 newtons, and the horizontal component is 145 newtons.

_____N
and the angle

Well, well, well! Looks like your friend took a tumble! Let's get those numbers straight, shall we? We have a vertical component of 140 Newtons, and a horizontal component of 145 Newtons. Now, to find the overall force, we can use a little mathematical magic!

First, let's find the angle. We can call it "angle of friendship rescue." To find it, we can use a little trigonometry. The tangent of the angle is equal to the vertical component divided by the horizontal component. So, tan(θ) = 140/145. Crunching those numbers, the angle is approximately 43.6 degrees.

Now, let's find the overall force, which we can call the "helping hand force." Using the Pythagorean theorem, we can find the magnitude of the force. The square of the overall force is equal to the sum of the squares of the horizontal and vertical components. So, F² = 140² + 145². A few calculations later, and we have F ≈ 200.68 Newtons.

So to recap: The angle is approximately 43.6 degrees, and the overall force is approximately 200.68 Newtons. Time to lend a hand and get your friend back on her feet!

To determine the angle, we can use trigonometry. The angle can be found using the inverse tangent function (tan⁻¹) of the ratio of the vertical component to the horizontal component.

tan⁻¹(Vertical Component/Horizontal Component) = Angle

Given that the vertical component is 140 Newtons and the horizontal component is 145 Newtons, we can calculate the angle as follows:

Angle = tan⁻¹(140/145)
Angle ≈ tan⁻¹(0.9655)
Angle ≈ 44.37 degrees.

Therefore, the angle is approximately 44.37 degrees.

To find the magnitude of the force, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the vertical component of the force (140 N) represents one side of the right triangle, and the horizontal component (145 N) represents the other side.

Using the Pythagorean theorem, you can calculate the magnitude of the force (hypotenuse):

Magnitude of the force = √(Vertical component^2 + Horizontal component^2)
Magnitude of the force = √(140^2 + 145^2)
Magnitude of the force = √(19600 + 21025)
Magnitude of the force = √(40625)
Magnitude of the force ≈ 201.57 N

So, the magnitude of the force you need to exert to help your friend up is approximately 201.57 Newtons.

Regarding the angle, you can use trigonometry to find it. The angle can be determined using the inverse tangent function (arctan or tan^(-1)).

Tangent of the angle = (Vertical component / Horizontal component)
Angle = arctan(Vertical component / Horizontal component)
Angle = arctan(140 / 145)
Angle ≈ 43.85 degrees

Thus, the angle between the force and the horizontal direction is approximately 43.85 degrees.

X = hor. = 145N.

Y = ver. = 140N.

tanA = Y / X = 140 / 145 = 0.9655,
A = 44 deg.

F = X / cosA = 145 / cos44 = 202N @ 44
deg.