To find out what would happen to the velocity of the basketball if its momentum is cut in half, we first need to know the formula for momentum:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
Given that the mass of the basketball is 1 kg and its initial velocity is 12 m/s, we can calculate the initial momentum:
\[ \text{Initial Momentum} = 1 , \text{kg} \times 12 , \text{m/s} = 12 , \text{kg m/s} \]
If the momentum is cut in half, the new momentum would be:
\[ \text{New Momentum} = \frac{12 , \text{kg m/s}}{2} = 6 , \text{kg m/s} \]
We can express the new momentum with the new velocity (\(v'\)):
\[ 6 , \text{kg m/s} = 1 , \text{kg} \times v' \]
To find \(v'\), we can rearrange this equation:
\[ v' = \frac{6 , \text{kg m/s}}{1 , \text{kg}} = 6 , \text{m/s} \]
So, if the momentum of the basketball were cut in half, its new velocity would be 6 m/s.
Since 6 m/s is half of the initial velocity of 12 m/s, the correct answer is:
It would be cut in half.
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