# A ball with a mass of #6 kg # and velocity of #5 m/s# collides with a second ball with a mass of #1 kg# and velocity of #- 7 m/s#. If #50%# of the kinetic energy is lost, what are the final velocities of the balls?

The velocities of the balls are

Energy is preserved

Thus,

Two equations with two unknowns each

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

- Conservation of momentum: (m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_{1f} + m_2 \cdot v_{2f})
- Equation for kinetic energy: (KE = \frac{1}{2}m_1v_{1}^2 + \frac{1}{2}m_2v_{2}^2)

Using these equations and given data, solve for the final velocities.

After solving, you'll find the final velocity of the first ball to be approximately 1.2 m/s and the final velocity of the second ball to be approximately -0.6 m/s.

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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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