# A ball with a mass of # 3# # kg# is rolling at #18 # #ms^-1# and elastically collides with a resting ball with a mass of #9 # #kg#. What are the post-collision velocities of the balls?

In an elastic collision, both momentum and kinetic energy are conserved. If we call the

First-movement momentum

First motion energy:

Given that this collision is elastic, both will be preserved:

Last-minute momentum

Last kinetic energy:

Next:

For neatness, let's multiply through by three:

Organizing:

Whether you solve using the quadratic formula or not, the result is:

This velocity is moving in the opposite direction of the initial velocity, as indicated by the minus sign.

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

Given: Mass of the first ball ((m_1)) = 3 kg Initial velocity of the first ball ((v_{1i})) = 18 m/s Mass of the second ball ((m_2)) = 9 kg Initial velocity of the second ball ((v_{2i})) = 0 m/s (at rest)

Let's denote the post-collision velocities as (v_{1f}) and (v_{2f}) for the first and second balls, respectively.

By conservation of momentum: [ m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f} ]

By conservation of kinetic energy: [ \frac{1}{2}m_1v_{1i}^2 + \frac{1}{2}m_2v_{2i}^2 = \frac{1}{2}m_1v_{1f}^2 + \frac{1}{2}m_2v_{2f}^2 ]

First, solve for the final velocity of the first ball ((v_{1f})) using the equations of conservation of momentum and kinetic energy.

Then, solve for the final velocity of the second ball ((v_{2f})) using the final velocity of the first ball.

After finding the values, we can determine the post-collision velocities of the balls.

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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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