A block with mass m₁ = 0.400 kg is released from rest on a frictionless track at a distance h₁ = 2.25 m above the top of a table. It then collides elastically with an object having mass m₂ = 0.800 kg that is initially at rest on the table, as shown in the figure below. m₂ h₂ m1 m2 (a) Determine the velocities of the two objects just after the collision. (Assume the positive direction is to the right. Indicate the direction with the signs of your answers.) m/s m/s (b) How high up the track does the 0.400-kg object travel back after the collision? m (c) How far away from the bottom of the table does the 0.800-kg object land, given that the height of the table is h₂ = 1.65 m? m (d) How far away from the bottom of the table does the 0.400-kg object eventually land? m

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Chapter1: Units, Trigonometry. And Vectors
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A block with mass \( m_1 = 0.400 \, \text{kg} \) is released from rest on a frictionless track at a distance \( h_1 = 2.25 \, \text{m} \) above the top of a table. It then collides elastically with an object having mass \( m_2 = 0.800 \, \text{kg} \) that is initially at rest on the table, as shown in the figure below.

**Diagram Description:**
- The diagram illustrates a track with a curved section where the block with mass \( m_1 \) is released.
- The height of the track from where the block starts is labeled \( h_1 = 2.25 \, \text{m} \).
- The second object \( m_2 \) is positioned on the flat section of the table.
- The table's height is marked as \( h_2 \).
- The distance \( x \) represents how far \( m_2 \) will land from the bottom of the table.

**Questions:**

(a) Determine the velocities of the two objects just after the collision. (Assume the positive direction is to the right. Indicate the direction with the signs of your answers.)
- \( v_1 = \) ____ m/s
- \( v_2 = \) ____ m/s

(b) How high up the track does the \( 0.400 \, \text{kg} \) object travel back after the collision?
- ____ m

(c) How far away from the bottom of the table does the \( 0.800 \, \text{kg} \) object land, given that the height of the table is \( h_2 = 1.65 \, \text{m} \)?
- ____ m

(d) How far away from the bottom of the table does the \( 0.400 \, \text{kg} \) object eventually land?
- ____ m
Transcribed Image Text:A block with mass \( m_1 = 0.400 \, \text{kg} \) is released from rest on a frictionless track at a distance \( h_1 = 2.25 \, \text{m} \) above the top of a table. It then collides elastically with an object having mass \( m_2 = 0.800 \, \text{kg} \) that is initially at rest on the table, as shown in the figure below. **Diagram Description:** - The diagram illustrates a track with a curved section where the block with mass \( m_1 \) is released. - The height of the track from where the block starts is labeled \( h_1 = 2.25 \, \text{m} \). - The second object \( m_2 \) is positioned on the flat section of the table. - The table's height is marked as \( h_2 \). - The distance \( x \) represents how far \( m_2 \) will land from the bottom of the table. **Questions:** (a) Determine the velocities of the two objects just after the collision. (Assume the positive direction is to the right. Indicate the direction with the signs of your answers.) - \( v_1 = \) ____ m/s - \( v_2 = \) ____ m/s (b) How high up the track does the \( 0.400 \, \text{kg} \) object travel back after the collision? - ____ m (c) How far away from the bottom of the table does the \( 0.800 \, \text{kg} \) object land, given that the height of the table is \( h_2 = 1.65 \, \text{m} \)? - ____ m (d) How far away from the bottom of the table does the \( 0.400 \, \text{kg} \) object eventually land? - ____ m
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