Rachel Pulls her 18 KG suitcase at at a constant speed by pulling on a handle that makes and angle (theta) with the Horizontal the frictional force of the suitcase is 27 N and Rachel exerts a 43 N force on the handle

What angle does the handle make with the horizontal?

The movement of the suitcase is afected only by the hor. component of

the force exerted by Rachel:

X = hor. = 43*cosA = 27,
cosA = 27/43 = 0.6279,
A = 51.1 Deg.

To find the angle (theta) that the handle makes with the horizontal, we can use the following formula:

tan(theta) = (frictional force)/(force exerted by Rachel)

Substituting the given values:

tan(theta) = 27 N / 43 N

Now, we can solve for theta by taking the inverse tangent (arctan) of both sides:

theta = atan(27 N / 43 N)

Using a calculator, we find:

theta ≈ 32.5 degrees

Therefore, the handle makes an angle of approximately 32.5 degrees with the horizontal.

To find the angle that the handle makes with the horizontal, we can use trigonometry. We know that Rachel exerts a force of 43 N on the handle, and there is a frictional force of 27 N acting against the motion of the suitcase.

The force exerted by Rachel can be broken down into two components: one parallel to the horizontal direction and one perpendicular to it. The component parallel to the horizontal direction is what overcomes the frictional force.

Let's denote the angle that the handle makes with the horizontal as θ. Since the speed of the suitcase is constant, we can assume that the net force acting on the suitcase is zero.

The force exerted by Rachel parallel to the horizontal direction can be found using trigonometry. It is given by:

Force_parallel = Force_exerted * cos(θ)

Since the net force is zero, the force parallel to the horizontal direction is equal to the frictional force:

Force_parallel = Frictional_force = 27 N

Now we can solve for θ:

27 N = 43 N * cos(θ)

Dividing both sides by 43 N:

cos(θ) = 27 N / 43 N

θ = arccos(27/43)

Using a calculator, we can find the value of θ to be approximately 46.86 degrees.

Therefore, the angle that the handle makes with the horizontal is approximately 46.86 degrees.