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A 8.2 kg ball moving with a velocity of 14.6 m/s collides with a 3.3 kg ball moving with a velocity of 4.3 m/s in the opposite direction. Find the common velocity of the balls (in m/s) if they coalesce on impact. (Enter the magnitude only)

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sqdancefan

Answer:

  9.18 m/s

Explanation:

Momentum is conserved.

The heavier ball has a momentum (arbitrarily defined as positive) of ...

  Mv = (8.2 kg)(14.6 m/s) = 119.72 kg·m/s

The lighter ball has a momentum of ...

  Mv = (3.3 kg)(-4.3 m/s) = -14.19 kg·m/s

So the total momentum is ...

  119.72 -14.19 = 105.53 . . . . kg·m/s

After the collision, the total mass is ...

  8.2 kg +3.3 kg = 11.5 kg

That mass with the total momentum has a velocity of ...

  (105.53 kg·m/s)/(11.5 kg) = 9.1765... m/s

The common velocity is about 9.18 m/s.