Certainly! Let's walk through the process of finding the dog's kinetic energy step-by-step.
The formula for kinetic energy (KE) is:
[tex]\[ KE = \frac{1}{2} \times m \times v^2 \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( v \)[/tex] is the velocity of the object (in meters per second).
Given:
- The dog's speed ([tex]\( v \)[/tex]) = 7 m/s.
- The dog's mass ([tex]\( m \)[/tex]) = 45 kg.
Substitute the given values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 45 \times (7)^2 \][/tex]
First, calculate the square of the speed:
[tex]\[ 7^2 = 49 \][/tex]
Next, multiply the mass by this squared speed:
[tex]\[ 45 \times 49 = 2205 \][/tex]
Now, take half of this product to find the kinetic energy:
[tex]\[ KE = \frac{2205}{2} = 1102.5 \][/tex]
So, the kinetic energy of the dog is:
[tex]\[ 1102.5 \, \text{J} \][/tex]
Therefore, the correct answer is:
D. 1102.5 J
