When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and, thus, slows him down. Suppose the weight of the sky diver is 986 N and the drag force has a magnitude of 1049 N. The mass of the sky diver is 101 kg. Take upward to be the positive direction. What is his acceleration, including sign?

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### Understanding the Forces Acting on a Sky Diver with an Open Parachute

**Concept of Drag Force and Acceleration in Skydiving**

When a parachute opens, the air exerts a large drag force on it. This upward force initially surpasses the weight of the sky diver and, hence, decelerates the descent. Here, we explore how to calculate the sky diver's acceleration using provided data.

**Problem Statement:**

Suppose the weight of the sky diver is **986 N** and the drag force has a magnitude of **1049 N**. The mass of the sky diver is **101 kg**. Taking upward to be the positive direction, we aim to determine the sky diver's acceleration, including the sign.

**Steps to Solve:**

1. **Identify the Forces:**
   - Weight (\( W \)) = 986 N (downward)
   - Drag Force (\( F_d \)) = 1049 N (upward)

2. **Net Force Calculation:**
   - Since upward is positive, the net force \( F_{\text{net}} \) is calculated as:
     \[
     F_{\text{net}} = F_d - W
     \]
     \[
     F_{\text{net}} = 1049 \, \text{N} - 986 \, \text{N} = 63 \, \text{N}
     \]

3. **Determine Acceleration:**
   Using Newton's second law \( F = ma \):
     \[
     a = \frac{F_{\text{net}}}{m}
     \]
   Given mass (\( m \)) = 101 kg:
     \[
     a = \frac{63 \, \text{N}}{101 \, \text{kg}} = 0.624 \, \text{m/s}^2
     \]
   Since the net force is positive, the acceleration is +0.624 m/s², indicating the sky diver is decelerating.

**Interactive Component:**

In an interactive screen section, students can input their calculated values to verify correctness. For example:

**Input Area:**
   - Number: **+0.624**
   - Units: **m/s²**
   
**Attempts:**
   - Attempts: **2 of 3 used**
   
**Submit Answer Button:**
   - An interactive **Submit Answer** button
Transcribed Image Text:### Understanding the Forces Acting on a Sky Diver with an Open Parachute **Concept of Drag Force and Acceleration in Skydiving** When a parachute opens, the air exerts a large drag force on it. This upward force initially surpasses the weight of the sky diver and, hence, decelerates the descent. Here, we explore how to calculate the sky diver's acceleration using provided data. **Problem Statement:** Suppose the weight of the sky diver is **986 N** and the drag force has a magnitude of **1049 N**. The mass of the sky diver is **101 kg**. Taking upward to be the positive direction, we aim to determine the sky diver's acceleration, including the sign. **Steps to Solve:** 1. **Identify the Forces:** - Weight (\( W \)) = 986 N (downward) - Drag Force (\( F_d \)) = 1049 N (upward) 2. **Net Force Calculation:** - Since upward is positive, the net force \( F_{\text{net}} \) is calculated as: \[ F_{\text{net}} = F_d - W \] \[ F_{\text{net}} = 1049 \, \text{N} - 986 \, \text{N} = 63 \, \text{N} \] 3. **Determine Acceleration:** Using Newton's second law \( F = ma \): \[ a = \frac{F_{\text{net}}}{m} \] Given mass (\( m \)) = 101 kg: \[ a = \frac{63 \, \text{N}}{101 \, \text{kg}} = 0.624 \, \text{m/s}^2 \] Since the net force is positive, the acceleration is +0.624 m/s², indicating the sky diver is decelerating. **Interactive Component:** In an interactive screen section, students can input their calculated values to verify correctness. For example: **Input Area:** - Number: **+0.624** - Units: **m/s²** **Attempts:** - Attempts: **2 of 3 used** **Submit Answer Button:** - An interactive **Submit Answer** button
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