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What is the velocity of a skateboarder whose momentum is [tex][tex]$100 \, \text{kg} \cdot \text{m/s}$[/tex][/tex] and mass is [tex][tex]$15 \, \text{kg}$[/tex][/tex]? Round to the nearest hundredth.

A. [tex][tex]$13.25 \, \text{m/s}$[/tex][/tex]
B. [tex][tex]$6.67 \, \text{m/s}$[/tex][/tex]
C. [tex][tex]$6.67 \, \text{kg}$[/tex][/tex]
D. [tex][tex]$3.33 \, \text{m/s}$[/tex][/tex]


Sagot :

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]