# A ball with a mass of #2 kg # and velocity of #6 m/s# collides with a second ball with a mass of #1 kg# and velocity of #- 3 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?

See below

firstly, momentum (

Or

In terms of KE (

.....the

These solve to give:

In terms of the second possible solution, for the first ball to have positive (right to left) velocity

In the first solution, both balls are travelling right to left, and the lighter ball is travelling with greater speed which conforms with intuition.

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For the 2 kg ball: 4.8 m/s, and for the 1 kg ball: -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.

- The kinetic energy of an object with a mass of #3 kg# constantly changes from #60 J# to #270 J# over #8 s#. What is the impulse on the object at #5 s#?
- A ball with a mass of #2kg# moving at #1 m/s# hits a still ball with a mass of #6 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of #6 kg# moving at #7 m/s# hits a still ball with a mass of #12 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of #5 kg# moving at #3 m/s# hits a still ball with a mass of #16 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of # 2 kg# is rolling at #5 m/s# and elastically collides with a resting ball with a mass of #9 kg#. What are the post-collision velocities of the balls?

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