# A ball with a mass of #3 kg # and velocity of #5 m/s# collides with a second ball with a mass of #7 kg# and velocity of #- 2 m/s#. If #25%# 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, we can use the principle of conservation of momentum and the equation for kinetic energy. First, calculate the total momentum before the collision. Then, use the given information about the percentage of kinetic energy lost to find the total kinetic energy after the collision. Finally, use the equations involving momentum and kinetic energy to solve for 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.

- A ball with a mass of #9 kg# moving at #15 m/s# hits a still ball with a mass of #2 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of #2kg# moving at #6 m/s# hits a still ball with a mass of #9 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of # 3 kg# is rolling at #16 m/s# and elastically collides with a resting ball with a mass of # 8 kg#. What are the post-collision velocities of the balls?
- A ball with a mass of #3 kg# moving at #1 m/s# hits a still ball with a mass of #7 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of #2 kg # and velocity of #4 m/s# collides with a second ball with a mass of #5 kg# and velocity of #- 6 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?

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