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

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To find the post-collision velocities of the balls, we can use the principle of conservation of momentum and kinetic energy. According to this principle, the total momentum and kinetic energy before the collision should be equal to the total momentum and kinetic energy after the collision.

Given: Mass of ball 1 (m1) = 5 kg Initial velocity of ball 1 (u1) = 5 m/s Mass of ball 2 (m2) = 2 kg Initial velocity of ball 2 (u2) = 0 m/s (since the ball is at rest)

Using conservation of momentum: m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

Using conservation of kinetic energy (since the collision is elastic): 0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

We have two equations and two unknowns (v1 and v2), which we can solve simultaneously to find the post-collision velocities of the balls. Plugging in the given values and solving the equations will give us the post-collision velocities.

After solving the equations, we find: v1 ≈ 1.364 m/s v2 ≈ 5.545 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.

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