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Answer :
To solve for the truck's mass with the given information, we'll follow these steps:
1. Understand the given values:
- The truck's momentum ([tex]\( p \)[/tex]) is [tex]\( 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex].
- The velocity ([tex]\( v \)[/tex]) of the truck is [tex]\( 22.0 \, \text{m/s} \)[/tex].
2. Know the relationship between momentum, mass, and velocity:
- The formula for momentum is:
[tex]\[
p = m \cdot v
\][/tex]
where [tex]\( m \)[/tex] is the mass of the truck.
3. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
- To find the mass, divide both sides of the equation by the velocity ([tex]\( v \)[/tex]):
[tex]\[
m = \frac{p}{v}
\][/tex]
4. Substitute the given values into the formula:
- Momentum ([tex]\( p \)[/tex]) is [tex]\(125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}\)[/tex].
- Velocity ([tex]\( v \)[/tex]) is [tex]\( 22.0 \, \text{m/s} \)[/tex].
So,
[tex]\[
m = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}}
\][/tex]
5. Perform the calculation:
[tex]\[
m = \frac{125,000}{22.0}
\][/tex]
[tex]\[
m \approx 5681.82 \, \text{kg}
\][/tex]
Thus, the mass of the truck is approximately [tex]\( 5681.82 \, \text{kg} \)[/tex].
Among the provided answer choices, the closest match is:
- 176 kg
- 2750 kg
- 5680 kg
- 11,400 kg
The correct one is [tex]\( 5680 \, \text{kg} \)[/tex]. This is the answer that best aligns with our calculated result.
1. Understand the given values:
- The truck's momentum ([tex]\( p \)[/tex]) is [tex]\( 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex].
- The velocity ([tex]\( v \)[/tex]) of the truck is [tex]\( 22.0 \, \text{m/s} \)[/tex].
2. Know the relationship between momentum, mass, and velocity:
- The formula for momentum is:
[tex]\[
p = m \cdot v
\][/tex]
where [tex]\( m \)[/tex] is the mass of the truck.
3. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
- To find the mass, divide both sides of the equation by the velocity ([tex]\( v \)[/tex]):
[tex]\[
m = \frac{p}{v}
\][/tex]
4. Substitute the given values into the formula:
- Momentum ([tex]\( p \)[/tex]) is [tex]\(125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}\)[/tex].
- Velocity ([tex]\( v \)[/tex]) is [tex]\( 22.0 \, \text{m/s} \)[/tex].
So,
[tex]\[
m = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}}
\][/tex]
5. Perform the calculation:
[tex]\[
m = \frac{125,000}{22.0}
\][/tex]
[tex]\[
m \approx 5681.82 \, \text{kg}
\][/tex]
Thus, the mass of the truck is approximately [tex]\( 5681.82 \, \text{kg} \)[/tex].
Among the provided answer choices, the closest match is:
- 176 kg
- 2750 kg
- 5680 kg
- 11,400 kg
The correct one is [tex]\( 5680 \, \text{kg} \)[/tex]. This is the answer that best aligns with our calculated result.
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