# A ball with a mass of #7 kg# moving at #4 m/s# hits a still ball with a mass of #12 kg#. If the first ball stops moving, how fast is the second ball moving?

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To find the velocity of the second ball after the collision, you can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

Momentum before collision = Momentum after collision

(m_1 \times v_1 + m_2 \times v_2 = (m_1 + m_2) \times v_f)

Where: (m_1 = 7) kg (mass of the first ball) (v_1 = 4) m/s (initial velocity of the first ball) (m_2 = 12) kg (mass of the second ball) (v_2 =) velocity of the second ball (to be found) (v_f = 0) m/s (final velocity, as the first ball stops moving)

(7 \times 4 + 12 \times v_2 = (7 + 12) \times 0)

(28 + 12 \times v_2 = 0)

(12 \times v_2 = -28)

(v_2 = \frac{-28}{12} = -\frac{7}{3} \approx -2.33) m/s

Therefore, the second ball is moving at approximately (2.33) m/s in the opposite direction.

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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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