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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. The formula is:

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

We are given the momentum and velocity of the truck, and we need to find the mass. We can rearrange the formula to solve for mass:

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

Given:
- Momentum = 125,000 kg·m/s
- Velocity = 22.0 m/s

Now, substitute the given values into the rearranged formula:

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

[tex]\[ \text{mass} = 5,681.818181818182 \, \text{kg} \][/tex]

Since we are selecting from given options, we will choose the closest one, which is 5680 kg. Therefore, the mass of the truck is approximately:

5680 kg

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