To determine the velocity of a skateboarder whose momentum is [tex]\(100 \, \text{kg} \cdot \text{m} / \text{s}\)[/tex] and mass is [tex]\(15 \, \text{kg}\)[/tex], we use the formula for momentum, which is given by:
[tex]\[ p = mv \][/tex]
where:
- [tex]\( p \)[/tex] is momentum
- [tex]\( m \)[/tex] is mass
- [tex]\( v \)[/tex] is velocity
We aim to find the velocity [tex]\( v \)[/tex]. Rearranging the formula to solve for [tex]\( v \)[/tex], we get:
[tex]\[ v = \frac{p}{m} \][/tex]
Substitute the given values into the equation:
[tex]\[ v = \frac{100 \, \text{kg} \cdot \text{m} / \text{s}}{15 \, \text{kg}} \][/tex]
Simplifying this:
[tex]\[ v = 6.666666666666667 \, \text{m} / \text{s} \][/tex]
To give the answer rounded to the nearest hundredth, we round [tex]\( 6.666666666666667 \)[/tex] to [tex]\( 6.67 \)[/tex].
Therefore, the velocity of the skateboarder is [tex]\( 6.67 \, \text{m} / \text{s} \)[/tex].
The correct answer is:
B. [tex]\( 6.67 \, \text{m} / \text{s} \)[/tex]
