Final answer:
The kinetic energy of a person with a mass of 87 grams running at a speed of 9.3 m/s is approximately 3.76 joules, using the formula KE = 1/2mv² and converting the mass from grams to kilograms.
Step-by-step explanation:
Calculating Kinetic Energy
To calculate the kinetic energy of a person running, we use the formula KE = 1/2mv², where KE represents kinetic energy, m is the mass in kilograms, and v is the velocity in meters per second. The given mass of 87 grams needs to be converted to kilograms (0.087 kg) since the SI unit of mass in the formula is kilograms. Using the provided velocity of 9.3 m/s, the calculation for kinetic energy will be KE = 1/2 × 0.087 kg × (9.3 m/s)².
Carrying out this calculation:
KE = 1/2 × 0.087 kg × 86.49 m²/s² = 3.763155 J
Thus, the kinetic energy of the person is approximately 3.76 joules.
Understanding the Joule
A joule is the SI unit of energy and is defined as 1 kilogram-meter²/second² (kg·m²/s²). To put this into perspective, an astronomy instructor with a mass of 73 kilograms running at 4.4 meters per second has a motion energy of about 700 joules.