# A ball with a mass of #7 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?

Use conservation of momentum relation

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To find the velocity of the second ball after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Momentum (p) is calculated as the product of mass (m) and velocity (v), so:

Total momentum before collision = Total momentum after collision

(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')

Given: m1 = 7 kg (mass of the first ball) v1 = 6 m/s (initial velocity of the first ball) m2 = 9 kg (mass of the second ball) v1' = 0 m/s (final velocity of the first ball, as it stops moving) v2' = v2 (final velocity of the second ball)

Substituting the given values into the equation:

(7 kg * 6 m/s) + (9 kg * 0 m/s) = (7 kg * 0 m/s) + (9 kg * v2)

Solving for v2:

42 kg*m/s = 0 kg*m/s + 9 kg * v2

42 kg*m/s = 9 kg * v2

v2 = 42 kg*m/s / 9 kg

v2 ≈ 4.67 m/s

So, the second ball is moving at approximately 4.67 m/s after the collision.

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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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