A ball with a mass of #4 kg # and velocity of #3 m/s# collides with a second ball with a mass of #2 kg# and velocity of # 1 m/s#. If #75%# 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 solve for the final velocities of the balls after the collision, you can use the principle of conservation of momentum and the equation for kinetic energy.
Let ( m_1 = 4 ) kg, ( v_1 = 3 ) m/s, ( m_2 = 2 ) kg, and ( v_2 = 1 ) m/s.

Conservation of momentum equation: [ m_1v_1 + m_2v_2 = m_1v_{1f} + m_2v_{2f} ]

Initial kinetic energy of the system: [ KE_{initial} = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 ]

Given that 75% of the kinetic energy is lost, the final kinetic energy of the system: [ KE_{final} = 0.25 \times KE_{initial} ]

Using the equation for kinetic energy: [ KE_{initial}  KE_{final} = \frac{1}{2}m_1v_{1f}^2 + \frac{1}{2}m_2v_{2f}^2 ]
Now, you can solve these equations to find the final velocities ( v_{1f} ) and ( v_{2f} ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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