Answer :
To find the velocity of the man, we will use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
Where:
- [tex]\( KE \)[/tex] is the kinetic energy.
- Mass is the mass of the object.
- Velocity is what we want to find out.
We are given:
- The mass of the man: 122 kg
- The kinetic energy: 306 J
First, rearrange the kinetic energy formula to solve for velocity:
[tex]\[ \text{velocity}^2 = \frac{2 \times KE}{\text{mass}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{velocity}^2 = \frac{2 \times 306}{122} \][/tex]
[tex]\[ \text{velocity}^2 = \frac{612}{122} \][/tex]
[tex]\[ \text{velocity}^2 = 5.01639344262 \][/tex]
Now, take the square root of both sides to find the velocity:
[tex]\[ \text{velocity} = \sqrt{5.01639344262} \][/tex]
[tex]\[ \text{velocity} \approx 2.24 \, \text{m/s} \][/tex]
So, the velocity of the man is approximately 2.24 meters per second.
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]
Where:
- [tex]\( KE \)[/tex] is the kinetic energy.
- Mass is the mass of the object.
- Velocity is what we want to find out.
We are given:
- The mass of the man: 122 kg
- The kinetic energy: 306 J
First, rearrange the kinetic energy formula to solve for velocity:
[tex]\[ \text{velocity}^2 = \frac{2 \times KE}{\text{mass}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{velocity}^2 = \frac{2 \times 306}{122} \][/tex]
[tex]\[ \text{velocity}^2 = \frac{612}{122} \][/tex]
[tex]\[ \text{velocity}^2 = 5.01639344262 \][/tex]
Now, take the square root of both sides to find the velocity:
[tex]\[ \text{velocity} = \sqrt{5.01639344262} \][/tex]
[tex]\[ \text{velocity} \approx 2.24 \, \text{m/s} \][/tex]
So, the velocity of the man is approximately 2.24 meters per second.
