Two spheres collide on a horizontal surface (all velocities, before and after the collision, are in the x-y plane). Throughout this problem, assume that all forces aside from those exerted by the spheres themselves are negligible (at least in comparison).Sphere A has a mass of 0.65 grams. It has an initial speed of 6.0 m/s and an initial velocity that is oriented at an angle of θ A i = 28 degrees below the x-axis.Sphere B has a mass of 0.45 grams. It has an initial speed of 6.5 m/s and an initial velocity that is oriented at an angle of θ B i = 35 degrees above the x-axis.After the collision, sphere A has a speed of 3.5 m/s and a velocity that is directed at an angle of θ A f = 16 degrees above the x-axis.What is the final speed, in units of meters per second, of sphere B? The image illustrates an initial and final state of a two-body interaction, likely a collision. It uses diagrams with vector representations to show momentum and direction.### Initial State- **Mass \( m_A \)** (yellow circle) - Velocity vector \( \vec{v}_{A,i} \) - Angle \( \theta_{A,i} \)- **Mass \( m_B \)** (green circle) - Velocity vector \( \vec{v}_{B,i} \) - Angle \( \theta_{B,i} \)### Final State- **Mass \( m_A \)** (yellow circle) - Velocity vector \( \vec{v}_{A,f} \) - Angle \( \theta_{A,f} \)- **Mass \( m_B \)** (green circle) - Velocity vector \( \vec{v}_{B,f} \) (indicated with a question mark, suggesting unknown or to be determined)### Coordinate System- A basic x-y coordinate system is centered between the initial and final states to provide a reference for angle and direction.This diagram is useful for analyzing the conservation of momentum and energy in physics problems, such as elastic or inelastic collisions.

When no net external force acts on the system then the total linear momentum of the system is…

Two spheres collide on a horizontal surface (all velocities, before and after the collision, are in the x-y plane). Throughout this problem, assume that all forces aside from those exerted by the spheres themselves are negligible (at least in comparison). Sphere A has a mass of 0.65 grams. It has an initial speed of 6.0 m/s and an initial velocity that is oriented at an angle of θ A i = 28 degrees below the x-axis. Sphere B has a mass of 0.45 grams. It has an initial speed of 6.5 m/s and an initial velocity that is oriented at an angle of θ B i = 35 degrees above the x-axis. After the collision, sphere A has a speed of 3.5 m/s and a velocity that is directed at an angle of θ A f = 16 degrees above the x-axis. What is the final speed, in units of meters per second, of sphere B?

Two spheres collide on a horizontal surface (all velocities, before and after the collision, are in the x-y plane). Throughout this problem, assume that all forces aside from those exerted by the spheres themselves are negligible (at least in comparison). Sphere A has a mass of 0.65 grams. It has an initial speed of 6.0 m/s and an initial velocity that is oriented at an angle of θ A i = 28 degrees below the x-axis. Sphere B has a mass of 0.45 grams. It has an initial speed of 6.5 m/s and an initial velocity that is oriented at an angle of θ B i = 35 degrees above the x-axis. After the collision, sphere A has a speed of 3.5 m/s and a velocity that is directed at an angle of θ A f = 16 degrees above the x-axis. What is the final speed, in units of meters per second, of sphere B?

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Question

Sphere A has a mass of 0.65 grams. It has an initial speed of 6.0 m/s and an initial velocity that is oriented at an angle of θ A i = 28 degrees below the x-axis.

Sphere B has a mass of 0.45 grams. It has an initial speed of 6.5 m/s and an initial velocity that is oriented at an angle of θ B i = 35 degrees above the x-axis.

After the collision, sphere A has a speed of 3.5 m/s and a velocity that is directed at an angle of θ A f = 16 degrees above the x-axis.

What is the final speed, in units of meters per second, of sphere B?

The image illustrates an initial and final state of a two-body interaction, likely a collision. It uses diagrams with vector representations to show momentum and direction.

### Initial State

- **Mass \( m_A \)** (yellow circle)
- Velocity vector \( \vec{v}_{A,i} \)
- Angle \( \theta_{A,i} \)

- **Mass \( m_B \)** (green circle)
- Velocity vector \( \vec{v}_{B,i} \)
- Angle \( \theta_{B,i} \)

### Final State

- **Mass \( m_A \)** (yellow circle)
- Velocity vector \( \vec{v}_{A,f} \)
- Angle \( \theta_{A,f} \)

- **Mass \( m_B \)** (green circle)
- Velocity vector \( \vec{v}_{B,f} \) (indicated with a question mark, suggesting unknown or to be determined)

### Coordinate System
- A basic x-y coordinate system is centered between the initial and final states to provide a reference for angle and direction.

This diagram is useful for analyzing the conservation of momentum and energy in physics problems, such as elastic or inelastic collisions.

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