Some object moves 220.0 m at an angle of 42° north of west. During this motion, a 68.0 N force acts on the same object, doing +5460.0 J of work on the object. Assuming the force is applied horizontal to ground, what is this force’s orientation? Is there more than one possible answer? Explain.

W=F•d•cosθ,

cosθ =W/F•d =
5460/68•220=0.365,
θ =arccos 0.65=68.6º
The force is applied at 68.6º with
the displacement or
with 360 º -68.6 with the displacement

To determine the force's orientation, we can use the concept of work done by a force and the angle between the force and the displacement.

The work done by a force can be calculated using the formula: work = force * displacement * cos(theta)

Given:
Work = +5460.0 J
Displacement = 220.0 m
Force = 68.0 N
Angle (theta) = 42° north of west

First, let's convert the angle measure to its component in the x-axis direction (east) and y-axis direction (north).

The x-component of the displacement (d_x) can be found by multiplying the displacement by the cosine of the angle:
d_x = displacement * cos(theta)
d_x = 220.0 m * cos(42°)

The y-component of the displacement (d_y) can be found by multiplying the displacement by the sine of the angle:
d_y = displacement * sin(theta)
d_y = 220.0 m * sin(42°)

Now, we can calculate the work done using the x-component of displacement and force:
work = force * d_x
5460.0 J = 68.0 N * d_x

Solving for d_x:
d_x = 5460.0 J / 68.0 N

Similarly, we can calculate the work done using the y-component of displacement and force:
work = force * d_y
5460.0 J = 68.0 N * d_y

Solving for d_y:
d_y = 5460.0 J / 68.0 N

Now, to find the orientation of the force, we can use the tangent of the angle (theta) as the ratio of the y-component to the x-component:
tan(theta) = d_y / d_x

Calculating the tangent of the angle:
tan(theta) = d_y / d_x

Substituting the values of d_x and d_y:
tan(theta) = (5460.0 J / 68.0 N) / (220.0 m * cos(42°) / 68.0 N)

Now, we can use the inverse tangent function to find the angle:
theta = arctan((5460.0 J / 68.0 N) / (220.0 m * cos(42°) / 68.0 N))

By solving this equation, we can find the orientation of the force.

However, let's consider if there could be more than one possible answer. In this case, since we have a force applied horizontally to the ground (the x-axis), the angle theta would determine the inclination of the force in the y-axis direction only. The horizontal component of the force will always be zero in this scenario. Therefore, there is only one possible answer for the force's orientation, which is the angle theta.