To find the mass of Sergei Bubka, we can use the relationship between potential energy (PE) and mass (m) given by the equation:
\[ PE = mgh \]
Where:
- \( PE \) is the potential energy (in joules)
- \( m \) is the mass (in kilograms)
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
- \( h \) is the height (in meters)
Given:
- The maximum potential energy \( PE = 4.80 , \text{kJ} = 4800 , \text{J} \)
- The height at the midpoint of the jump can be considered half the total jump height, so \( h = \frac{6.13 , \text{m}}{2} = 3.065 , \text{m} \)
We can rearrange the formula to solve for mass \( m \):
\[ m = \frac{PE}{gh} \]
Now, substituting in the known values:
\[ m = \frac{4800 , \text{J}}{9.81 , \text{m/s}^2 \times 3.065 , \text{m}} \]
Calculating the denominator:
\[ 9.81 \times 3.065 \approx 30.1 , \text{m}^2/\text{s}^2 \]
Now substituting this back in:
\[ m \approx \frac{4800}{30.1} \approx 159.73 , \text{kg} \]
Thus, Sergei Bubka's mass is approximately:
\[ \boxed{160 , \text{kg}} \]