Final answer:
To have the same kinetic energy as a 68 kg sprinter running at 9 m/s, a 2,890 kg elephant must move at approximately 0.71 m/s.
Step-by-step explanation:
Determining the Speed of the Elephant to Match the Sprinter's Kinetic Energy
To calculate how fast a 2,890 kg elephant must move to have the same kinetic energy (KE) as a 68 kg sprinter running at 9 m/s, we use the formula for kinetic energy: KE = 1/2 × m × v^2, where m is mass and v is velocity. Given that the kinetic energies are equal, we set the kinetic energy of the sprinter equal to the kinetic energy of the elephant, solving for the elephant's velocity:
1/2 × (68 kg) × (9 m/s)^2 = 1/2 × (2,890 kg) × v^2
After simplifying and solving for v, the velocity of the elephant is:
v = sqrt((68 kg × (9 m/s)^2) / 2,890 kg)
When we calculate this, we find that the elephant must move at a velocity of approximately 0.71 m/s to match the kinetic energy of the sprinter running at 9 m/s.