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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

Answer :

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

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

We are given the momentum and the velocity of the truck, and we need to solve for its mass. Let's set up the equation with the given values:

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

To solve for the mass, we can rearrange the formula:

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

By substituting the given values into the equation, we get:

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

When you calculate this, the mass comes out to be:

[tex]\[ \text{mass} \approx 5681.818 \, \text{kg} \][/tex]

Since the question asks for the closest value from the options given, we should select the nearest whole number:

The best answer is 5680 kg.

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