Question

Though slow on land, the leatherback turtle holds the record for the fastest water speed of any reptile: 9.78
m/s. It is also among the largest of reptiles. Suppose the largest leatherback yet discovered were to swim
at the top leatherback speed. If its kinetic energy was 6.08 × 104 J, what was its mass?

Answer 1

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:

\[
\boxed{1270.12 \, kg}
\]