To determine the speed of a dog with a given mass and kinetic energy, we start with the formula for kinetic energy:
[tex]\[ \text{Kinetic Energy (KE)} = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( v \)[/tex] is the speed.
Given:
- [tex]\( m = 14 \)[/tex] kg (mass of the dog),
- [tex]\( KE = 135.5 \)[/tex] J (kinetic energy of the dog).
We need to solve for [tex]\( v \)[/tex]. To do that, we rearrange the formula to isolate [tex]\( v \)[/tex]:
[tex]\[ v^2 = \frac{2 \cdot KE}{m} \][/tex]
Substitute the known values into the equation:
[tex]\[ v^2 = \frac{2 \cdot 135.5}{14} \][/tex]
Next, simplify the expression inside the square root:
[tex]\[ v^2 = \frac{271}{14} \][/tex]
Calculate the division:
[tex]\[ v^2 = 19.3571 \][/tex]
Now, take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{19.3571} \][/tex]
[tex]\[ v \approx 4.399675312695569 \][/tex]
Therefore, the speed of the dog is approximately [tex]\( 4.4 \, \text{m/s} \)[/tex].
Thus, the correct answer is:
A. [tex]\( 4.4 \, \text{m/s} \)[/tex]
