To solve this problem, we need to calculate the momentum for each object. Momentum ([tex]\(p\)[/tex]) is given by the formula:
[tex]\[ p = m \times v \][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(v\)[/tex] is the velocity of the object.
Let's calculate the momentum for each object:
1. Object W:
- Mass [tex]\( = 12 \)[/tex] kg
- Velocity [tex]\( = 5 \)[/tex] m/s
- Momentum [tex]\( = 12 \times 5 = 60 \)[/tex] kg·m/s
2. Object X:
- Mass [tex]\( = 15 \)[/tex] kg
- Velocity [tex]\( = 8 \)[/tex] m/s
- Momentum [tex]\( = 15 \times 8 = 120 \)[/tex] kg·m/s
3. Object Y:
- Mass [tex]\( = 18 \)[/tex] kg
- Velocity [tex]\( = 2 \)[/tex] m/s
- Momentum [tex]\( = 18 \times 2 = 36 \)[/tex] kg·m/s
4. Object Z:
- Mass [tex]\( = 28 \)[/tex] kg
- Velocity [tex]\( = 10 \)[/tex] m/s
- Momentum [tex]\( = 28 \times 10 = 280 \)[/tex] kg·m/s
Now that we have calculated the momentum for each object, we can list them in increasing order of their momentum:
- Momentum of [tex]\( Y = 36 \)[/tex] kg·m/s
- Momentum of [tex]\( W = 60 \)[/tex] kg·m/s
- Momentum of [tex]\( X = 120 \)[/tex] kg·m/s
- Momentum of [tex]\( Z = 280 \)[/tex] kg·m/s
Hence, the correct order from least to greatest momentum is:
[tex]\[ Y, W, X, Z \][/tex]
Therefore, the correct answer is:
[tex]\[ D) \; Y, W, X, Z \][/tex]
