# A ball with a mass of # 5# #kg# is rolling at #4# #ms^-1# and elastically collides with a resting ball with a mass of #3# #kg#. What are the post-collision velocities of the balls?

Momentum is always conserved, and the key word 'elastically' tells us that kinetic energy is also conserved. The calculation below shows how we determine the final velocities of the balls, which are

For momentum:

For kinetic energy:

We can substitute in the known masses to make these simpler:

To make it even a little neater, let's multiply equation B' by 2:

Expanding the square:

Subtract 80 from both sides and rearrange:

Multiplying through by 5 (I hate fractions):

Substituting back into A':

We can substitute these values back into A and B to check them.

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The post-collision velocities are 2 m/s for the 5 kg ball and 6 m/s for the 3 kg ball.

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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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- How much momentum does a #2 kg# object moving at #15 m/s# have?
- A ball with a mass of #11# #kg# moving at #18# #ms^-1# hits a still ball with a mass of #22# #kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
- A ball with a mass of #5 kg # and velocity of #8 m/s# collides with a second ball with a mass of #2 kg# and velocity of #- 6 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?

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