A 60 kg package is falling downward with an acceleration of 3.00 m/s² when its velocity is 30.0 m/s. It is known that the drag force is significant and is equal to F, = bv². a) Draw the free body diagram and kinetic diagram b) Determine the drag coefficient, b ( include units). c) Determine the terminal velocity of the package.

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**Problem Statement:**

A 60 kg package is falling downward with an acceleration of \(3.00 \, \text{m/s}^2\) when its velocity is \(30.0 \, \text{m/s}\). It is known that the drag force is significant and is equal to \( F_D = b v^2 \).

a) Draw the free body diagram and kinetic diagram.

b) Determine the drag coefficient, \( b \) (include units).

c) Determine the terminal velocity of the package.

**Instructions for Educational Context:**

- **Free Body Diagram and Kinetic Diagram:**
  - **Free Body Diagram:** Illustrate the forces acting on the package including the gravitational force (\(mg\)) and the drag force (\(F_D\)).
  - **Kinetic Diagram:** Show the directions of the velocity and acceleration vectors, indicating that the net force results in a downward acceleration of \(3.00 \, \text{m/s}^2\).

- **Calculating the Drag Coefficient \(b\):**
  - Use Newton's second law \( F_{\text{net}} = ma \), where \( F_{\text{net}} = mg - F_D \).
  - Substitute known values and solve for \( b \).

- **Determining Terminal Velocity:**
  - Terminal velocity occurs when acceleration is zero, meaning \( mg = F_D \).
  - Use the drag force equation \( mg = b v_t^2 \) and solve for \( v_t \).
Transcribed Image Text:**Problem Statement:** A 60 kg package is falling downward with an acceleration of \(3.00 \, \text{m/s}^2\) when its velocity is \(30.0 \, \text{m/s}\). It is known that the drag force is significant and is equal to \( F_D = b v^2 \). a) Draw the free body diagram and kinetic diagram. b) Determine the drag coefficient, \( b \) (include units). c) Determine the terminal velocity of the package. **Instructions for Educational Context:** - **Free Body Diagram and Kinetic Diagram:** - **Free Body Diagram:** Illustrate the forces acting on the package including the gravitational force (\(mg\)) and the drag force (\(F_D\)). - **Kinetic Diagram:** Show the directions of the velocity and acceleration vectors, indicating that the net force results in a downward acceleration of \(3.00 \, \text{m/s}^2\). - **Calculating the Drag Coefficient \(b\):** - Use Newton's second law \( F_{\text{net}} = ma \), where \( F_{\text{net}} = mg - F_D \). - Substitute known values and solve for \( b \). - **Determining Terminal Velocity:** - Terminal velocity occurs when acceleration is zero, meaning \( mg = F_D \). - Use the drag force equation \( mg = b v_t^2 \) and solve for \( v_t \).
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