# A ball with a mass of # 3 kg# is rolling at #8 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

The post collision velocities are

In an elastic collision, there is conservation of momentum and conservation of kinetic energies.

Here,

The masses are

The initial velocities are

So,

This is the initial conditions.

or

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To find the post-collision velocities, you can use the principle of conservation of momentum and the coefficient of restitution. First, calculate the total momentum before the collision using the formula (p = m_1v_1 + m_2v_2), where (m_1) and (m_2) are the masses of the two balls, and (v_1) and (v_2) are their respective velocities. Then, use the same equation to find the total momentum after the collision. Since it's an elastic collision, you can also use the equation (e = \frac{{v_{2f} - v_{1f}}}{{v_{1i} - v_{2i}}}), where (e) is the coefficient of restitution, (v_{1i}) and (v_{2i}) are the initial velocities of the two balls, and (v_{1f}) and (v_{2f}) are their final velocities. Rearrange the equation to solve for (v_{1f}) and (v_{2f}). Substituting the known values, solve for the final velocities.

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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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