# A ball with a mass of # 5 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of #3 kg#. What are the post-collision velocities of the balls?

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

- Calculate the total momentum before the collision.
- Apply the conservation of momentum to find the velocities of the balls after the collision.
- Apply the conservation of kinetic energy to check if the collision is elastic.

Let ( v_1 ) be the velocity of the 5 kg ball after the collision, and ( v_2 ) be the velocity of the 3 kg ball after the collision.

Conservation of momentum: ( m_1v_{1i} + m_2v_{2i} = m_1v_1 + m_2v_2 )

Conservation of kinetic energy: ( \frac{1}{2}m_1v_{1i}^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 )

Given: ( m_1 = 5 ) kg, ( v_{1i} = 6 ) m/s ( m_2 = 3 ) kg, ( v_{2i} = 0 ) m/s (resting)

Conservation of momentum: ( 5(6) + 3(0) = 5v_1 + 3v_2 ) ( 30 = 5v_1 + 3v_2 ) ...........(1)

Conservation of kinetic energy: ( \frac{1}{2}(5)(6)^2 = \frac{1}{2}(5)v_1^2 + \frac{1}{2}(3)v_2^2 ) ( 90 = 15v_1^2 + \frac{3}{2}v_2^2 ) ...........(2)

Solve equations (1) and (2) simultaneously to find ( v_1 ) and ( v_2 ).

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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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