# A ball with a mass of # 5 kg# is rolling at #18 m/s# and elastically collides with a resting ball with a mass of #3 kg#. What are the post-collision velocities of the balls?

Given

By conservation of momentum

Again the collision being elastic one the relative velocity of one ball with respect to the other is reversed by the collision and we get

By [1] and [2] we get

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(v_1 = \frac{m_1 - m_2}{m_1 + m_2} \cdot u_1 + \frac{2m_2}{m_1 + m_2} \cdot u_2)

(v_2 = \frac{2m_1}{m_1 + m_2} \cdot u_1 + \frac{m_2 - m_1}{m_1 + m_2} \cdot u_2)

Substitute the values:

(v_1 = \frac{5 - 3}{5 + 3} \cdot 18 + \frac{2 \cdot 3}{5 + 3} \cdot 0)

(v_2 = \frac{2 \cdot 5}{5 + 3} \cdot 18 + \frac{3 - 5}{5 + 3} \cdot 0)

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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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