To find the height of Stefka Kostadinova's high jump record, we can use the formula that relates gravitational potential energy (PE) to height (h):
\[ PE = mgh \]
where:
- \( PE \) is the potential energy,
- \( m \) is the mass,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height.
The ratio of potential energy to mass is given as:
\[ \frac{PE}{m} = gh \]
We know from the problem that this ratio is \( 20.482 , \text{m}^2/\text{s}^2 \). Therefore, we can set:
\[ gh = 20.482 , \text{m}^2/\text{s}^2 \]
Now, we can express height \( h \) as:
\[ h = \frac{20.482}{g} \]
Substituting the standard value for \( g \):
\[ h = \frac{20.482}{9.81} \]
Calculating this gives:
\[ h \approx \frac{20.482}{9.81} \approx 2.09 , \text{m} \]
Thus, the height of Stefka Kostadinova's record jump is approximately \( 2.09 , \text{meters} \).
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