To find the magnitude of the retarding force acting on the meteor, we can start by applying Newton's second law of motion, which states that the net force acting on an object is equal to the mass of that object multiplied by its acceleration. In this case, the meteor is experiencing two forces: the gravitational force pulling it downward and the retarding force acting upward due to atmospheric drag. Let's break this down step by step.

Identifying the Forces

First, let's identify the forces acting on the meteor:

• Weight of the meteor (W): This is the force due to gravity, calculated as \( W = m \cdot g \), where \( m \) is the mass of the meteor (0.25 kg) and \( g \) is the acceleration due to gravity (approximately 9.81 m/s² on Earth).
• Retarding force (F_d): This is the upward force due to air resistance that opposes the weight of the meteor.

Calculating Gravitational Force

Now, let's calculate the weight of the meteor:

Using the formula:

W = m * g

W = 0.25 kg * 9.81 m/s² = 2.4525 N

Applying Newton's Second Law

Next, we can apply Newton's second law. The net force (F_net) acting on the meteor can be expressed as:

F_net = W - F_d

Since the meteor is falling with an acceleration of 9.2 m/s², we can also express the net force in terms of mass and acceleration:

F_net = m * a

F_net = 0.25 kg * 9.2 m/s² = 2.3 N

Finding the Retarding Force

Now we can set these two expressions for net force equal to each other:

W - F_d = m * a

2.4525 N - F_d = 2.3 N

Rearranging this equation allows us to find the retarding force:

F_d = W - m * a

F_d = 2.4525 N - 2.3 N = 0.1525 N

Conclusion

The magnitude of the retarding force acting on the meteor due to atmospheric drag is approximately 0.1525 N. This force is crucial in understanding how objects behave when they fall through fluids, as it significantly influences their acceleration and terminal velocity.