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.
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 \( v_t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc51bbc5c-2db3-4ce7-b17e-b374d3b9eb8f%2F5ecb4919-1b5a-4dbf-bbc5-3d15e43f5df7%2Fmovxuha_processed.jpeg&w=3840&q=75)
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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