Lacyqtpieidn
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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 15 kg? Round to the nearest hundredth.

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

Sagot :

GinnyAnsweridn
To determine the velocity of a skateboarder given their momentum and mass, we can use the formula for momentum:

[tex]\[ \text{Momentum} = \text{Mass} \times \text{Velocity} \][/tex]

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

We need to find the velocity ([tex]\( v \)[/tex]). Rearrange the momentum formula to solve for velocity:

[tex]\[ v = \frac{p}{m} \][/tex]

Substitute in the given values:

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

Divide to obtain the velocity:

[tex]\[ v = \frac{100}{15} = 6.67 \, \text{m/s} \][/tex]

Rounding to the nearest hundredth, the calculated velocity is 6.67 m/s.

Thus, the best answer is:

D. [tex]$6.67 \, \text{m/s}$[/tex]
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