(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.

Solution:

The translational kinetic energy of an object of mass m moving at speed v is KE=\frac{1}{2}mv^{2}.

Part A. The Velocity of the Elephant to have the same Kinetic Energy as the Sprinter

First, we need to solve for the kinetic energy of the sprinter.

\begin{align*}
KE_{\text{sprinter}} & = \frac{1}{2} \left( 65.0\ \text{kg} \right)\left( 10.0\ \text{m}/\text{s} \right)^{2} \\
KE_{\text{sprinter}} & = 3250\ \text{J}
\end{align*}

Then, we need to equate this to the kinetic energy of the elephant with the velocity as the unknown.

\begin{align*}
KE_{\text{elephant}} & = KE_{\text{sprinter}} \\
\frac{1}{2}\left( 3000\ \text{kg} \right) v^{2} & = 3250\ \text{J} \\
1500 v^{2} & = 3250 \\
v^{2} & = \frac{3250}{1500} \\
v & = \sqrt[]{\frac{3250}{1500}} \\
v & = 1.4720\ \text{m}/\text{s} \\
v & = 1.47\ \text{m}/\text{s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Part B. How Larger Energies Needed for the Movement of Larger Animals would Relate to Metabolic Rates

If the elephant and the sprinter accelerate to a final velocity of 10.0 m/s, then
the elephant would have a much larger kinetic energy than the sprinter.
Therefore, the elephant clearly has burned more energy and requires a faster
metabolic output to sustain that speed. \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)