(30) A man drops a $$ 2.7 \cdot \mathrm{~kg} $$ bag out a window 11 meters above ground to his friend, 1.7 meters above ground. Determine the velocity of the bag just before it reaches his friend's hands. Notebook

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To determine the velocity of the bag just before it reaches the friend's hands, we can analyze the problem using the principles of kinematics under free fall. Here's a step-by-step solution:

### **Given:**
- **Mass of the bag (m):** $$ 2.7 \, \text{kg} $$ *(Note: The mass is not required for calculating velocity in free fall without air resistance.)*
- **Initial height above ground (h₁):** $$ 11 \, \text{meters} $$
- **Final height above ground (h₂):** $$ 1.7 \, \text{meters} $$
- **Acceleration due to gravity (g):** $$ 9.81 \, \text{m/s}² $$

### **Steps:**

1. **Calculate the Drop Distance (Δh):**
   
   $$
   \Delta h = h₁ - h₂ = 11 \, \text{m} - 1.7 \, \text{m} = 9.3 \, \text{meters}
   $$
   
2. **Determine Initial Velocity (u):**
   
   Since the bag is **dropped**, its initial velocity $$ u = 0 \, \text{m/s} $$.

3. **Use the Kinematic Equation:**
   
   The final velocity $$ v $$ can be found using the equation:
   
   $$
   v² = u² + 2g\Delta h
   $$
   
   Plugging in the known values:
   
   $$
   v² = 0 + 2 \times 9.81 \, \text{m/s}² \times 9.3 \, \text{m}
   $$
   
   $$
   v² = 182.466 \, \text{m²/s²}
   $$
   
4. **Solve for $$ v $$:**
   
   $$
   v = \sqrt{182.466} \approx 13.5 \, \text{m/s}
   $$
   
   *(For a more precise calculation: $$ v \approx 13.51 \, \text{m/s} $$)*

### **Conclusion:**

The velocity of the bag just before it reaches the friend's hands is approximately **13.5 meters per second**.

**Final Answer:**  
The bag strikes the friend’s hands with a velocity of approximately 13.5 m s⁻¹.
The bag reaches the friend's hands with a velocity of approximately 13.5 meters per second.

(30) A man drops a bag out a window 11 meters above ground to his friend, 1.7 meters above ground. Determine the velocity of the bag just before it reaches his friend’s hands.

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(30) A man drops a bag out a window 11 meters above ground to his friend, 1.7 meters above ground. Determine the velocity of the bag just before it reaches his friend’s hands. Notebook