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Answer :
Let's solve the problem step-by-step to find the mass of the truck.
First, we need to understand the relationship between momentum, mass, and velocity. The formula for momentum ([tex]\( p \)[/tex]) is:
[tex]\[ p = m \cdot v \][/tex]
where [tex]\( p \)[/tex] is the momentum, [tex]\( m \)[/tex] is the mass, and [tex]\( v \)[/tex] is the velocity.
We are given:
- The momentum [tex]\( p \)[/tex] is [tex]\( 125,000 \, \text{kg} \cdot \text{m/s} \)[/tex]
- The velocity [tex]\( v \)[/tex] is [tex]\( 22.0 \, \text{m/s} \)[/tex]
Our goal is to find the mass ([tex]\( m \)[/tex]) of the truck. We can rearrange the formula to solve for mass:
[tex]\[ m = \frac{p}{v} \][/tex]
Plugging the given values into the formula, we get:
[tex]\[ m = \frac{125,000 \, \text{kg} \cdot \text{m/s}}{22.0 \, \text{m/s}} \][/tex]
When we perform this division:
[tex]\[ m = 5681.818181818182 \, \text{kg} \][/tex]
Rounding to the nearest whole number, we get:
[tex]\[ m \approx 5682 \, \text{kg} \][/tex]
So, the truck's mass is closest to:
[tex]\[ \boxed{5680 \, \text{kg}} \][/tex]
This matches the provided answer options, making [tex]\( 5680 \, \text{kg} \)[/tex] the correct choice.
First, we need to understand the relationship between momentum, mass, and velocity. The formula for momentum ([tex]\( p \)[/tex]) is:
[tex]\[ p = m \cdot v \][/tex]
where [tex]\( p \)[/tex] is the momentum, [tex]\( m \)[/tex] is the mass, and [tex]\( v \)[/tex] is the velocity.
We are given:
- The momentum [tex]\( p \)[/tex] is [tex]\( 125,000 \, \text{kg} \cdot \text{m/s} \)[/tex]
- The velocity [tex]\( v \)[/tex] is [tex]\( 22.0 \, \text{m/s} \)[/tex]
Our goal is to find the mass ([tex]\( m \)[/tex]) of the truck. We can rearrange the formula to solve for mass:
[tex]\[ m = \frac{p}{v} \][/tex]
Plugging the given values into the formula, we get:
[tex]\[ m = \frac{125,000 \, \text{kg} \cdot \text{m/s}}{22.0 \, \text{m/s}} \][/tex]
When we perform this division:
[tex]\[ m = 5681.818181818182 \, \text{kg} \][/tex]
Rounding to the nearest whole number, we get:
[tex]\[ m \approx 5682 \, \text{kg} \][/tex]
So, the truck's mass is closest to:
[tex]\[ \boxed{5680 \, \text{kg}} \][/tex]
This matches the provided answer options, making [tex]\( 5680 \, \text{kg} \)[/tex] the correct choice.
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