# A ball with a mass of # 5 kg# is rolling at #3 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?

By signing up, you agree to our Terms of Service and Privacy Policy

Using the conservation of linear momentum and the principles of elastic collisions:

[ m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_{1f} + m_2 \cdot v_{2f} ]

[ v_{1f} = \frac{(m_1 - m_2) \cdot v_{1i} + 2 \cdot m_2 \cdot v_{2i}}{m_1 + m_2} ]

[ v_{2f} = \frac{2 \cdot m_1 \cdot v_{1i} + (m_2 - m_1) \cdot v_{2i}}{m_1 + m_2} ]

Substitute the given values:

[ v_{1f} = \frac{(5 - 2) \cdot 3 + 2 \cdot 2 \cdot 0}{5 + 2} ]

[ v_{2f} = \frac{2 \cdot 5 \cdot 3 + (2 - 5) \cdot 0}{5 + 2} ]

[ v_{1f} \approx 1.57 \ \text{m/s} ]

[ v_{2f} \approx 2.29 \ \text{m/s} ]

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws a #20 kg# object at a speed of #5 m/s#, how much will his speed change by?
- 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 #- 8 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?
- A ball with a mass of #4 kg# 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? How much kinetic energy was lost as heat in the collision?
- A ball with a mass of #2kg# moving at #8 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?
- An astronaut with a mass of #85 kg# is floating in space. If the astronaut throws a #17 kg# object at a speed of #15 m/s#, how much will his speed change by?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7