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Answer :
Sure! Let's solve this step by step.
1. Identify the given values:
- Momentum (p) = 125,000 kg⋅m/s
- Velocity (v) = 22.0 m/s
2. Recall the formula for momentum:
Momentum is calculated using the formula:
[tex]\[
p = m \cdot v
\][/tex]
Where [tex]\( p \)[/tex] is momentum, [tex]\( m \)[/tex] is mass, and [tex]\( v \)[/tex] is velocity.
3. Rearrange the formula to solve for mass:
To find the mass ([tex]\( m \)[/tex]), we rearrange the formula to:
[tex]\[
m = \frac{p}{v}
\][/tex]
4. Substitute the given values into the equation:
[tex]\[
m = \frac{125,000 \, \text{kg} \cdot \frac{m}{s}}{22.0 \, \frac{m}{s}}
\][/tex]
5. Perform the division:
[tex]\[
m = \frac{125,000}{22.0} \approx 5681.82 \, \text{kg}
\][/tex]
6. Approximate the result to match the given options:
[tex]\[
m \approx 5680 \, \text{kg}
\][/tex]
So, the truck's mass, rounded to match the given choices, is approximately 5680 kg.
Therefore, the correct answer is:
[tex]\[
5680 \, \text{kg}
\][/tex]
1. Identify the given values:
- Momentum (p) = 125,000 kg⋅m/s
- Velocity (v) = 22.0 m/s
2. Recall the formula for momentum:
Momentum is calculated using the formula:
[tex]\[
p = m \cdot v
\][/tex]
Where [tex]\( p \)[/tex] is momentum, [tex]\( m \)[/tex] is mass, and [tex]\( v \)[/tex] is velocity.
3. Rearrange the formula to solve for mass:
To find the mass ([tex]\( m \)[/tex]), we rearrange the formula to:
[tex]\[
m = \frac{p}{v}
\][/tex]
4. Substitute the given values into the equation:
[tex]\[
m = \frac{125,000 \, \text{kg} \cdot \frac{m}{s}}{22.0 \, \frac{m}{s}}
\][/tex]
5. Perform the division:
[tex]\[
m = \frac{125,000}{22.0} \approx 5681.82 \, \text{kg}
\][/tex]
6. Approximate the result to match the given options:
[tex]\[
m \approx 5680 \, \text{kg}
\][/tex]
So, the truck's mass, rounded to match the given choices, is approximately 5680 kg.
Therefore, the correct answer is:
[tex]\[
5680 \, \text{kg}
\][/tex]
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