Sure, let's solve this step-by-step.
We start with the equation for kinetic energy:
[tex]\[ E_k = \frac{1}{2}mv^2 \][/tex]
where,
- [tex]\( E_k \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( v \)[/tex] is the velocity.
Given values:
- Kinetic energy, [tex]\( E_k \)[/tex] = 148 Joules
- Mass, [tex]\( m \)[/tex] = 30 kg
We need to solve for the velocity [tex]\( v \)[/tex].
First, rearrange the kinetic energy formula to solve for [tex]\( v \)[/tex]:
[tex]\[ E_k = \frac{1}{2}mv^2 \][/tex]
Multiply both sides by 2 to get rid of the 1/2 term:
[tex]\[ 2E_k = mv^2 \][/tex]
Now, divide both sides by [tex]\( m \)[/tex]:
[tex]\[ v^2 = \frac{2E_k}{m} \][/tex]
Take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2E_k}{m}} \][/tex]
Substitute the given values (E_k = 148 J and m = 30 kg) into the equation:
[tex]\[ v = \sqrt{\frac{2 \times 148}{30}} \][/tex]
Calculate the value inside the square root first:
[tex]\[ \frac{2 \times 148}{30} = \frac{296}{30} \approx 9.87 \][/tex]
Now, take the square root of 9.87:
[tex]\[ v = \sqrt{9.87} \approx 3.14 \][/tex]
Thus, the speed of the jaguar is approximately:
[tex]\[ v \approx 3.14 \, \text{m/s} \][/tex]
So, the jaguar is moving at a speed of approximately 3.14 meters per second.
