An air track glider with mass 0.60 kg moves with velocity 0.7 m/s to the right. At the same time, another glider with mass 0.29 kg from the other end of the air track moves with a velocity of -0.4 m/s (negative indicates to the left). Immediately after the two collide and couple together with Velcro tape, how fast are the gliders? Include negative sign if your answer is negative, to indicate they are moving to the left.

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**Physics Problem: Colliding Gliders on an Air Track**

**Problem Statement:**

An air track glider with mass 0.60 kg moves with velocity 0.7 m/s to the right. At the same time, another glider with mass 0.29 kg from the other end of the air track moves with a velocity of -0.4 m/s (negative indicates to the left). Immediately after the two collide and couple together with Velcro tape, how fast are the gliders?

Include negative sign if your answer is negative, to indicate they are moving to the left.

---

**Solution Approach:**

You can solve this problem using the principle of conservation of momentum. 

**Formulas and Steps:**

1. **Conservation of Momentum:**
   \( (m_1 \times v_1) + (m_2 \times v_2) = (m_1 + m_2) \times v_f \)

   Where:
   - \( m_1 \) = mass of the first glider
   - \( v_1 \) = velocity of the first glider
   - \( m_2 \) = mass of the second glider
   - \( v_2 \) = velocity of the second glider
   - \( v_f \) = final velocity of both gliders after collision

2. **Input Values:**
   \( m_1 = 0.60 \) kg
   \( v_1 = 0.7 \) m/s
   \( m_2 = 0.29 \) kg
   \( v_2 = -0.4 \) m/s

3. **Plug in the Values:**

   \[
   (0.60 \times 0.7) + (0.29 \times -0.4) = (0.60 + 0.29) \times v_f
   \]

4. **Calculate:**

   \[
   (0.42) + (-0.116) = 0.89 \times v_f
   \]

   \[
   0.304 = 0.89 \times v_f
   \]

   \[
   v_f = \frac{0.304}{0.89} \approx 0.34 \text{ m/s}
   \]

5. **Result:**
   The final velocity (\
Transcribed Image Text:**Physics Problem: Colliding Gliders on an Air Track** **Problem Statement:** An air track glider with mass 0.60 kg moves with velocity 0.7 m/s to the right. At the same time, another glider with mass 0.29 kg from the other end of the air track moves with a velocity of -0.4 m/s (negative indicates to the left). Immediately after the two collide and couple together with Velcro tape, how fast are the gliders? Include negative sign if your answer is negative, to indicate they are moving to the left. --- **Solution Approach:** You can solve this problem using the principle of conservation of momentum. **Formulas and Steps:** 1. **Conservation of Momentum:** \( (m_1 \times v_1) + (m_2 \times v_2) = (m_1 + m_2) \times v_f \) Where: - \( m_1 \) = mass of the first glider - \( v_1 \) = velocity of the first glider - \( m_2 \) = mass of the second glider - \( v_2 \) = velocity of the second glider - \( v_f \) = final velocity of both gliders after collision 2. **Input Values:** \( m_1 = 0.60 \) kg \( v_1 = 0.7 \) m/s \( m_2 = 0.29 \) kg \( v_2 = -0.4 \) m/s 3. **Plug in the Values:** \[ (0.60 \times 0.7) + (0.29 \times -0.4) = (0.60 + 0.29) \times v_f \] 4. **Calculate:** \[ (0.42) + (-0.116) = 0.89 \times v_f \] \[ 0.304 = 0.89 \times v_f \] \[ v_f = \frac{0.304}{0.89} \approx 0.34 \text{ m/s} \] 5. **Result:** The final velocity (\
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