To solve this problem, we need to calculate the momentum for each object. Momentum is given by the formula:
[tex]\[ \text{Momentum} = \text{Mass} \times \text{Velocity} \][/tex]
Let's calculate the momentum for each object one by one.
1. Object W:
- Mass of W = 12 kg
- Velocity of W = 5 m/s
- Momentum of W = [tex]\( 12 \, \text{kg} \times 5 \, \text{m/s} = 60 \, \text{kg}\cdot\text{m/s} \)[/tex]
2. Object X:
- Mass of X = 15 kg
- Velocity of X = 8 m/s
- Momentum of X = [tex]\( 15 \, \text{kg} \times 8 \, \text{m/s} = 120 \, \text{kg}\cdot\text{m/s} \)[/tex]
3. Object Y:
- Mass of Y = 18 kg
- Velocity of Y = 2 m/s
- Momentum of Y = [tex]\( 18 \, \text{kg} \times 2 \, \text{m/s} = 36 \, \text{kg}\cdot\text{m/s} \)[/tex]
4. Object Z:
- Mass of Z = 28 kg
- Velocity of Z = 10 m/s
- Momentum of Z = [tex]\( 28 \, \text{kg} \times 10 \, \text{m/s} = 280 \, \text{kg}\cdot\text{m/s} \)[/tex]
Now, we have the momentum values for each object:
- [tex]\( \text{Momentum of W} = 60 \, \text{kg}\cdot\text{m/s} \)[/tex]
- [tex]\( \text{Momentum of X} = 120 \, \text{kg}\cdot\text{m/s} \)[/tex]
- [tex]\( \text{Momentum of Y} = 36 \, \text{kg}\cdot\text{m/s} \)[/tex]
- [tex]\( \text{Momentum of Z} = 280 \, \text{kg}\cdot\text{m/s} \)[/tex]
To list the objects in order from least to greatest momentum, we organize these values:
1. [tex]\( \text{Momentum of Y} = 36 \, \text{kg}\cdot\text{m/s} \)[/tex]
2. [tex]\( \text{Momentum of W} = 60 \, \text{kg}\cdot\text{m/s} \)[/tex]
3. [tex]\( \text{Momentum of X} = 120 \, \text{kg}\cdot\text{m/s} \)[/tex]
4. [tex]\( \text{Momentum of Z} = 280 \, \text{kg}\cdot\text{m/s} \)[/tex]
Thus, the objects in order from least to greatest momentum are:
[tex]\[ Y, W, X, Z \][/tex]
So, the correct answer is:
[tex]\[ \boxed{Y, W, X, Z} \][/tex]
