10. An object (A) of mass mA = 17.5 kg is moving due west with a speed VA = 8.10 m/s, while object (B) of mass mg 28.0 kg is moving in a direction that makes angle of 46° south of west with a speed VB = 5.15 m/s. The two objects collide and stick together in a completely inelastic collision. Find the magnitude of the final velocity of the two-object system after the collision. m/s

Principles of Physics: A Calculus-Based Text
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Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom
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### Problem Statement

**Question 10:**

An object (A) of mass \( m_A = 17.5 \) kg is moving due west with a speed \( v_A = 8.10 \) m/s, while object (B) of mass \( m_B = 28.0 \) kg is moving in a direction that makes an angle of \( 46^\circ \) south of west with a speed \( v_B = 5.15 \) m/s. The two objects collide and stick together in a completely inelastic collision. 

**Objective:**

Find the magnitude of the final velocity of the two-object system after the collision.

**Solution:**

Given data:
- Mass of object A, \( m_A = 17.5 \) kg
- Velocity of object A, \( v_A = 8.10 \) m/s (due west)
- Mass of object B, \( m_B = 28.0 \) kg
- Velocity of object B, \( v_B = 5.15 \) m/s at an angle of \( 46^\circ \) south of west

**Approach:**
1. Break down the velocities into their respective components.
2. Use the principle of conservation of momentum to find the final velocity of the combined mass after collision.

Place your answer in the box below:

\[ \boxed{\phantom{a}} \; \text{m/s} \]
Transcribed Image Text:### Problem Statement **Question 10:** An object (A) of mass \( m_A = 17.5 \) kg is moving due west with a speed \( v_A = 8.10 \) m/s, while object (B) of mass \( m_B = 28.0 \) kg is moving in a direction that makes an angle of \( 46^\circ \) south of west with a speed \( v_B = 5.15 \) m/s. The two objects collide and stick together in a completely inelastic collision. **Objective:** Find the magnitude of the final velocity of the two-object system after the collision. **Solution:** Given data: - Mass of object A, \( m_A = 17.5 \) kg - Velocity of object A, \( v_A = 8.10 \) m/s (due west) - Mass of object B, \( m_B = 28.0 \) kg - Velocity of object B, \( v_B = 5.15 \) m/s at an angle of \( 46^\circ \) south of west **Approach:** 1. Break down the velocities into their respective components. 2. Use the principle of conservation of momentum to find the final velocity of the combined mass after collision. Place your answer in the box below: \[ \boxed{\phantom{a}} \; \text{m/s} \]
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