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Answer :
To find the mass of the truck, we use the formula for momentum:
[tex]\[ \text{Momentum} = \text{mass} \times \text{velocity} \][/tex]
Given:
- The momentum of the truck is [tex]\( 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex].
- The velocity of the truck is [tex]\( 22.0 \, \text{m/s} \)[/tex].
We need to solve for the mass, so we rearrange the equation to find:
[tex]\[ \text{mass} = \frac{\text{Momentum}}{\text{velocity}} \][/tex]
Substitute the given values into the equation:
[tex]\[ \text{mass} = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}} \][/tex]
When you perform this division, the mass of the truck is approximately [tex]\( 5681.818 \, \text{kg} \)[/tex].
Since the answer should match one of the given options, we round this value to the nearest whole number, which is [tex]\( 5682 \, \text{kg} \)[/tex]. However, since the options provided in the question are:
- 176 kg
- 2750 kg
- 5680 kg
- [tex]\( 11,400 \, \text{kg} \)[/tex]
The closest to our computed value is [tex]\( 5680 \, \text{kg} \)[/tex].
Therefore, the truck's mass is approximately [tex]\( 5680 \, \text{kg} \)[/tex].
[tex]\[ \text{Momentum} = \text{mass} \times \text{velocity} \][/tex]
Given:
- The momentum of the truck is [tex]\( 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex].
- The velocity of the truck is [tex]\( 22.0 \, \text{m/s} \)[/tex].
We need to solve for the mass, so we rearrange the equation to find:
[tex]\[ \text{mass} = \frac{\text{Momentum}}{\text{velocity}} \][/tex]
Substitute the given values into the equation:
[tex]\[ \text{mass} = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}} \][/tex]
When you perform this division, the mass of the truck is approximately [tex]\( 5681.818 \, \text{kg} \)[/tex].
Since the answer should match one of the given options, we round this value to the nearest whole number, which is [tex]\( 5682 \, \text{kg} \)[/tex]. However, since the options provided in the question are:
- 176 kg
- 2750 kg
- 5680 kg
- [tex]\( 11,400 \, \text{kg} \)[/tex]
The closest to our computed value is [tex]\( 5680 \, \text{kg} \)[/tex].
Therefore, the truck's mass is approximately [tex]\( 5680 \, \text{kg} \)[/tex].
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