To solve for the mass of the stone flung by the catapult, we need to use the formula for kinetic energy:
[tex]\[ \text{KE} = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\(\text{KE}\)[/tex] is the kinetic energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(v\)[/tex] is the velocity.
We are given:
- [tex]\(\text{KE} = 1792 \, \text{J}\)[/tex]
- [tex]\(v = 16 \, \text{m/s}\)[/tex]
Our goal is to find the mass [tex]\(m\)[/tex]. We can rearrange the kinetic energy formula to solve for [tex]\(m\)[/tex]:
[tex]\[ m = \frac{2 \cdot \text{KE}}{v^2} \][/tex]
Let's go through the steps to find the mass:
1. Calculate [tex]\(v^2\)[/tex]:
[tex]\[ v^2 = 16^2 = 256 \, \text{m}^2/\text{s}^2 \][/tex]
2. Calculate [tex]\(2 \cdot \text{KE}\)[/tex]:
[tex]\[ 2 \cdot \text{KE} = 2 \cdot 1792 \, \text{J} = 3584 \, \text{J} \][/tex]
3. Calculate the mass [tex]\(m\)[/tex]:
[tex]\[ m = \frac{2 \cdot \text{KE}}{v^2} = \frac{3584 \, \text{J}}{256 \, \text{m}^2/\text{s}^2} = 14 \, \text{kg} \][/tex]
Therefore, the mass of the stone is [tex]\(14 \, \text{kg}\)[/tex].
The correct answer is:
[tex]\[ \boxed{14 \, \text{kg}} \][/tex]
