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A large truck is moving at [tex]22.0 \, \text{m/s}[/tex]. If its momentum is [tex]125,000 \, \text{kg} \cdot \text{m/s}[/tex], what is the truck's mass?

A. 176 kg
B. 2750 kg
C. 5680 kg
D. [tex]11,400 \, \text{kg}[/tex]

Answer :

To find the mass of the truck, we can use the formula for momentum:

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

We are given:
- Momentum = [tex]\( 125,000 \, \text{kg} \cdot \text{m/s} \)[/tex]
- Velocity = [tex]\( 22.0 \, \text{m/s} \)[/tex]

We need to solve for the mass, so we rearrange the formula to:

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

Now, substitute the given values into the formula:

[tex]\[ \text{mass} = \frac{125,000 \, \text{kg} \cdot \text{m/s}}{22.0 \, \text{m/s}} \][/tex]

[tex]\[ \text{mass} = 5681.818181818182 \, \text{kg} \][/tex]

This result rounds to approximately 5680 kg, which matches the choice given:

5680 kg

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