# A ball with a mass of #2 kg# is rolling at #3 m/s# and elastically collides with a resting ball with a mass of #1 kg#. What are the post-collision velocities of the balls?

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

To find the post-collision velocities of the balls, we can use the principle of conservation of momentum and kinetic energy. Let ( v_1 ) and ( v_2 ) be the velocities of the 2 kg and 1 kg balls respectively after the collision. We have the following equations:

- Conservation of momentum: [ m_1v_1 + m_2v_2 = m_1u_1 + m_2u_2 ]
- Conservation of kinetic energy (since it's an elastic collision): [ \frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 ]

Substituting the given values: [ 2 \times 3 + 1 \times 0 = 2 \times u_1 + 1 \times 0 ] [ \frac{1}{2} \times 2 \times 3^2 + \frac{1}{2} \times 1 \times 0^2 = \frac{1}{2} \times 2 \times v_1^2 + \frac{1}{2} \times 1 \times v_2^2 ]

Solving these equations simultaneously, we find: [ u_1 = 1 , \text{m/s} ] [ v_1 = 2 , \text{m/s} ] [ v_2 = 4 , \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.

- A 90 kg man is standing still on frictionless ice. His friend tosses him a 10 kg ball, which has a horizontal velocity of 20 m/s. After catching the ball, what is the man's velocity?
- 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 #- 1 m/s#. If #25%# of the kinetic energy is lost, what are the final velocities of the balls?
- During a collision, does an object always encounters an impulse and a change in momentum?
- How does friction affect conservation of momentum?
- A bullet traveling at 250 meters per second is brought to rest by an impulse of 5.00 newton-seconds. What is the mass of the bullet?

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