To determine the speed of the dog, we will use the formula for kinetic energy. The kinetic energy (KE) of an object is given by the equation:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
In this scenario, we are given:
- The mass ([tex]\(m\)[/tex]) of the dog is 14 kg.
- The kinetic energy ([tex]\(KE\)[/tex]) is 135.5 Joules.
We need to find the velocity ([tex]\(v\)[/tex]). Let's rearrange the kinetic energy equation to solve for velocity:
[tex]\[ KE = \frac{1}{2} \times m \times v^2 \][/tex]
First, multiply both sides of the equation by 2 to get rid of the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ 2 \times KE = m \times v^2 \][/tex]
Substitute the given values into the equation:
[tex]\[ 2 \times 135.5 = 14 \times v^2 \][/tex]
[tex]\[ 271 = 14 \times v^2 \][/tex]
Next, divide both sides by 14 to solve for [tex]\(v^2\)[/tex]:
[tex]\[ v^2 = \frac{271}{14} \][/tex]
[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]
Rounding this to one decimal place, we get:
[tex]\[ v \approx 4.4 \text{ m/s} \][/tex]
So the speed of the dog is approximately 4.4 m/s.
Therefore, the correct answer is:
OA. 4.4 m/s
