To find the mass of the leatherback turtle, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2} m v^2 \]
Where:
- \( KE \) is the kinetic energy (in joules),
- \( m \) is the mass (in kilograms),
- \( v \) is the velocity (in meters per second).
Given:
- \( KE = 6.08 \times 10^4 , J \)
- \( v = 9.78 , m/s \)
We can rearrange the formula to solve for mass \( m \):
\[ m = \frac{2 \cdot KE}{v^2} \]
Now substituting in the known values:
\[ m = \frac{2 \cdot 6.08 \times 10^4 , J}{(9.78 , m/s)^2} \]
Calculating the denominator:
\[ (9.78 , m/s)^2 = 95.4884 , m^2/s^2 \]
Now substituting this back into the mass formula:
\[ m = \frac{2 \cdot 6.08 \times 10^4 , J}{95.4884 , m^2/s^2} \]
Calculating the numerator:
\[ 2 \cdot 6.08 \times 10^4 , J = 1.216 \times 10^5 , J \]
Now dividing:
\[ m = \frac{1.216 \times 10^5 , J}{95.4884 , m^2/s^2} \approx 1270.12 , kg \]
Thus, the mass of the leatherback turtle is approximately:
\[ \boxed{1270.12 , kg} \]