High School

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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 \frac{\text{m}}{\text{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 = 125,000 kg·m/s
- Velocity = 22.0 m/s

We need to solve for the mass (m). Rearranging the formula to solve for mass gives:

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

Now, plug in the given values:

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

[tex]\[ \text{mass} = 5,681.82 \, \text{kg} \][/tex]

After calculating, we find that the truck's mass is approximately 5,681.82 kg. This rounds to 5,680 kg according to the choices provided.

Therefore, the correct answer is 5680 kg.

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