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Answer :
Sure! Let's break down the problem step by step to find the truck's mass.
We are given:
- The truck's momentum, [tex]\( p = 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex]
- The truck's velocity, [tex]\( v = 22.0 \, \text{m/s} \)[/tex]
To find the mass of the truck, we can use the formula for momentum:
[tex]\[ p = m \cdot v \][/tex]
Where:
- [tex]\( p \)[/tex] is the momentum
- [tex]\( m \)[/tex] is the mass
- [tex]\( v \)[/tex] is the velocity
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula, we get:
[tex]\[ m = \frac{p}{v} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}} \][/tex]
Now, perform the division:
[tex]\[ m \approx 5681.818 \, \text{kg} \][/tex]
Looking at the provided options:
1. 176 kg
2. 2750 kg
3. 5680 kg
4. 11,400 kg
The closest value to our calculated mass [tex]\( 5681.818 \, \text{kg} \)[/tex] is:
[tex]\[ \boxed{5680 \, \text{kg}} \][/tex]
So, the mass of the truck is approximately [tex]\( 5680 \, \text{kg} \)[/tex].
We are given:
- The truck's momentum, [tex]\( p = 125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex]
- The truck's velocity, [tex]\( v = 22.0 \, \text{m/s} \)[/tex]
To find the mass of the truck, we can use the formula for momentum:
[tex]\[ p = m \cdot v \][/tex]
Where:
- [tex]\( p \)[/tex] is the momentum
- [tex]\( m \)[/tex] is the mass
- [tex]\( v \)[/tex] is the velocity
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula, we get:
[tex]\[ m = \frac{p}{v} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{125,000 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{22.0 \, \text{m/s}} \][/tex]
Now, perform the division:
[tex]\[ m \approx 5681.818 \, \text{kg} \][/tex]
Looking at the provided options:
1. 176 kg
2. 2750 kg
3. 5680 kg
4. 11,400 kg
The closest value to our calculated mass [tex]\( 5681.818 \, \text{kg} \)[/tex] is:
[tex]\[ \boxed{5680 \, \text{kg}} \][/tex]
So, the mass of the truck is approximately [tex]\( 5680 \, \text{kg} \)[/tex].
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