# A ball with a mass of # 2 kg# is rolling at #2 m/s# and elastically collides with a resting ball with a mass of #9 kg#. What are the post-collision velocities of the balls?

The initially moving ball would move

(NOTE: The final velocity of an arbitrary object is indicated by velocities with apostrophes.)

Examine the system's overall momentum.

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To find the post-collision velocities of the balls, we can use the conservation of momentum and the conservation of kinetic energy.

Let ( v_1 ) be the velocity of the 2 kg ball after the collision and ( v_2 ) be the velocity of the 9 kg ball after the collision.

From the conservation of momentum:

[ m_1v_1 + m_2v_2 = m_1u_1 + m_2u_2 ]

where ( m_1 = 2 ) kg, ( m_2 = 9 ) kg, ( u_1 = 2 ) m/s, and ( u_2 = 0 ) m/s.

From the conservation of kinetic energy:

[ \frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 ]

Solving these equations simultaneously, we can find ( v_1 ) and ( v_2 ).

After solving, we get ( v_1 = 1.1 ) m/s and ( v_2 = 0.33 ) m/s.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- A block(1) of mass, m1= 3.2 kg, moving at speed 0.85 m/s hits another block (2) m2=2.7 kg at rest. After collision, both blocks stick and slide together on frictionless surface at the same speed. how to find the ratio of Kinetic energy (final/initial) ?
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