A person pushes a 16.0-kg shopping cart at a constant velocity for a distance of 20.0 m. She pushes in a direction 28.0° below the horizontal. A 54.0-N frictional force opposes the motion of the cart.

Wc = m * g = 16kg * 9.8N/kg = 156.8 N. = Wt. of the cart.

Fe*cos28-Ff = m*a
0.8829Fe - 54 = m*0 = 0
0.8829Fe = 54
Fe = 61.2 N. = Force exerted.

W = Fe*cos28 * d
W = 61.2*cos28 * 20 = 1080 Joules = Work
done on cart.

To solve this problem, we need to break down the forces acting on the shopping cart and use some basic physics principles. Let's break it down step-by-step:

Step 1: Identify the forces:
We have two forces acting on the shopping cart: the force of the person pushing the cart and the frictional force opposing the motion. The force of the person can be further broken down into horizontal and vertical components. The vertical component is perpendicular to the direction of motion and doesn't affect the motion of the cart.

Step 2: Find the horizontal component of the force:
To find the horizontal component of the force, we need to use trigonometry. Since the angle is given as 28.0° below the horizontal, the angle between the horizontal component and the total force is 90° - 28.0° = 62.0°.
Using the trigonometric identity: cos(θ) = adj/hypotenuse, we can find the horizontal component as:
cos(62.0°) = horizontal component/total force
horizontal component = cos(62.0°) * total force

Step 3: Calculate the horizontal component of the force:
Given that the total force is the force of the person pushing the cart, we can write:
total force = force of the person
horizontal component = cos(62.0°) * total force

Step 4: Find the net force acting on the cart:
The net force acting on the cart is the difference between the force of the person and the frictional force. Since the cart is moving at a constant velocity, the net force must be zero. Therefore, we can write:
net force = force of the person - frictional force
0 = force of the person - frictional force

Step 5: Calculate the force of the person:
Rearranging the equation from the previous step, we can solve for the force of the person:
force of the person = frictional force

Step 6: Calculate the work done by the person:
The work done by a force is given by the equation: work = force x distance x cos(θ), where θ is the angle between the force and the displacement.
Since the cart is moving at a constant velocity, the work done by the force of the person is equal to the work done by the frictional force. Therefore, we can calculate the work done by the person as:
work = force of the person x distance x cos(θ)
Note that the distance traveled by the cart is given as 20.0 m, and the angle θ is 28.0°.

Step 7: Calculate the work done by the frictional force:
Using the same equation as before, we can calculate the work done by the frictional force as:
work = frictional force x distance x cos(θ)

Step 8: Calculate the work done by the person (force of the person x distance x cos(θ)):
work = force of the person x distance x cos(θ)

Step 9: Calculate the work done by the frictional force (frictional force x distance x cos(θ)):
work = frictional force x distance x cos(θ)

Step 10: Compare the work done by the person and the frictional force:
Since the work done by the person is equal to the work done by the frictional force (as explained in Step 6), we can write:
force of the person x distance x cos(θ) = frictional force x distance x cos(θ)

Step 11: Cancel out the distance and cos(θ) terms:
Since the distance and cos(θ) terms appear on both sides of the equation, we can cancel them out. This leaves us with:
force of the person = frictional force

Step 12: Substitute in the given values and solve for the force of the person:
Given that the frictional force is 54.0 N, we can substitute it into the equation:
force of the person = 54.0 N

Therefore, the force of the person pushing the shopping cart is 54.0 N.

To solve this problem, we need to consider the forces acting on the shopping cart and use Newton's laws of motion.

First, let's analyze the forces acting on the cart:

1. The force applied by the person pushing the cart: This force has two components based on the given angle. The horizontal component doesn't contribute to the vertical motion of the cart, so we only consider the vertical component which helps the cart maintain a constant vertical velocity.

2. The force of friction opposing the motion: This force acts in the direction opposite to the motion of the cart. We are given its magnitude, which is 54.0 N.

Now, let's break down the forces acting on the cart in the vertical direction:

1. Force applied by the person: The vertical component of the applied force can be found by multiplying the total applied force by the sine of the angle. So, F_applied = F_total * sin(angle).

2. Force of friction: It opposes the motion, so its direction is opposite to the applied force. Therefore, the force of friction is -54.0 N.

Since the cart is moving at a constant velocity, the net force acting on it is zero. So, the force applied by the person must balance out the force of friction:

F_net = F_applied + F_friction = 0

Since F_net is zero, we can substitute the values:

F_applied - 54.0 N = 0

Solving for F_applied:

F_applied = 54.0 N

Now, let's calculate the force applied by the person:

F_applied = F_total * sin(angle)

So,

F_total * sin(angle) = 54.0 N

To calculate the total applied force (F_total):

F_total = F_applied / sin(angle)

F_total = 54.0 N / sin(28.0°)

Now, substitute the value of F_total into the equation and calculate it:

F_total = 54.0 N / sin(28.0°)

F_total ≈ 111.05 N

Therefore, the total force applied by the person pushing the shopping cart is approximately 111.05 N.