# A ball with a mass of #5 kg # and velocity of #6 m/s# collides with a second ball with a mass of #3 kg# and velocity of #- 7 m/s#. If #40%# of the kinetic energy is lost, what are the final velocities of the balls?

The final velocities are

We have conservation of momentum

The kinetic[energy is

Therefore,

and

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To find the final velocities of the balls after the collision, we can use the principle of conservation of momentum and the equation for kinetic energy.

First, we calculate the initial momentum of the system:

(p_{\text{initial}} = m_1v_1 + m_2v_2)

Next, we use the conservation of momentum to find the final momentum of the system:

(p_{\text{final}} = p_{\text{initial}})

Then, we calculate the initial kinetic energy of the system:

(KE_{\text{initial}} = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2)

Given that 40% of the kinetic energy is lost, the final kinetic energy can be expressed as:

(KE_{\text{final}} = (1 - 0.40) \times KE_{\text{initial}})

Finally, we use the final kinetic energy to find the final velocities of the balls using the equation for kinetic energy:

(KE_{\text{final}} = \frac{1}{2}m_1v_{1f}^2 + \frac{1}{2}m_2v_{2f}^2)

By solving these equations simultaneously, we can determine the final 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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- What is the recoil velocity of the gun?

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