# A ball with a mass of # 5 kg# is rolling at #7 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

I found:

Thus:

Combining the two equations yields the following result:

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To find the post-collision velocities, you can use the conservation of momentum and kinetic energy.

Let ( v_1 ) be the velocity of the 5 kg ball after the collision and ( v_2 ) be the velocity of the 4 kg ball after the collision.

Conservation of momentum: ( m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_1 + m_2 \cdot v_2 ) (5 \cdot 7 + 4 \cdot 0 = 5 \cdot v_1 + 4 \cdot v_2 )

Conservation of kinetic energy: ( \frac{1}{2} m_1 \cdot v_{1i}^2 = \frac{1}{2} m_1 \cdot v_1^2 + \frac{1}{2} m_2 \cdot v_2^2 ) ( \frac{1}{2} \cdot 5 \cdot 7^2 = \frac{1}{2} \cdot 5 \cdot v_1^2 + \frac{1}{2} \cdot 4 \cdot v_2^2 )

Solve these two equations to find ( v_1 ) and ( v_2 ).

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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 #4 kg # and velocity of #3 m/s# collides with a second ball with a mass of #2 kg# and velocity of #- 4 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?
- A ball with a mass of #2 kg# moving at #3 m/s# hits a still ball with a mass of #8 kg#. If the first ball stops moving, how fast is the second ball moving?
- A ball with a mass of #5 kg# moving at #20 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?
- Which has more momentum, a #5# #kg# object moving at #16# #ms^-1# or a #5# #kg# object moving at #20# #ms^-1#?
- An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #7 kg# object at a speed of #4 m/s#, how much will his speed change by?

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