Answered

The chart shows masses and velocities of four objects.

Motion of Four Objects

\begin{tabular}{|l|c|c|}
\hline Object & Mass (kg) & Velocity [tex]$( m / s )$[/tex] \\
\hline W & 12 & 5 \\
\hline [tex]$X$[/tex] & 15 & 8 \\
\hline [tex]$Y$[/tex] & 18 & 2 \\
\hline [tex]$Z$[/tex] & 28 & 10 \\
\hline
\end{tabular}

Which lists the objects in order, from least to greatest momentum?

A. [tex]$W, X, Y, Z$[/tex]

B. [tex]$Z, Y, X, W$[/tex]

C. [tex]$Z, X, W, Y$[/tex]

D. [tex]$Y, W, X, Z$[/tex]



Answer :

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]