Question

a basketball has a mass of 1 kg and is traveling 12 m/s. what would happen to the velocity if the momentum of the basketball were cut in half?
○ it would be cut in half.
○ it would be tripled.
○ it would be the same.
○ it would be doubled.

Explanation:

Step1: Recall the momentum formula

The formula for momentum is \( p = mv \), where \( p \) is momentum, \( m \) is mass, and \( v \) is velocity.

Step2: Analyze the effect of changing momentum

Given the mass \( m \) of the basketball remains constant (since we're not changing the basketball's mass, just its momentum/velocity). From \( p = mv \), we can rearrange it as \( v=\frac{p}{m} \). If \( m \) is constant, velocity \( v \) is directly proportional to momentum \( p \) (i.e., \( v\propto p \) when \( m \) is constant). So if momentum \( p \) is cut in half, and \( m \) stays the same, velocity \( v \) must also be cut in half (because \( v \) and \( p \) have a direct proportionality with constant \( m \)).

Answer:

It would be cut in half.