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

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

Sagot :

GinnyAnsweridn
To determine the velocity of the skateboarder, we can use the formula for momentum:

[tex]\[ \text{momentum} = \text{mass} \times \text{velocity} \][/tex]

Rearranging this formula to solve for velocity gives us:

[tex]\[ \text{velocity} = \frac{\text{momentum}}{\text{mass}} \][/tex]

Given:
- Momentum ([tex]\( p \)[/tex]) = 100 kg·m/s
- Mass ([tex]\( m \)[/tex]) = 15 kg

We can plug these values into the formula:

[tex]\[ \text{velocity} = \frac{100 \, \text{kg·m/s}}{15 \, \text{kg}} \][/tex]

[tex]\[ \text{velocity} = \frac{100}{15} \][/tex]

[tex]\[ \text{velocity} \approx 6.6667 \, \text{m/s} \][/tex]

Next, we round the calculated velocity to the nearest hundredth:

[tex]\[ \text{velocity} \approx 6.67 \, \text{m/s} \][/tex]

So, the correct answer is:

C) [tex]\(6.67 \, \text{m/s}\)[/tex]
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