Final answer:
The kinetic energy of a 23.2 g piece of space debris traveling at 81.9 m/s is calculated using the formula KE = (1/2)mv², resulting in a kinetic energy of 77.8 J.
Step-by-step explanation:
The kinetic energy of an object can be calculated using the formula KE = (1/2)mv², where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
To find the kinetic energy of a 23.2 g piece of space debris traveling at 81.9 m/s, first convert the mass from grams to kilograms (since the standard unit for mass in this equation is kilograms):
23.2 g = 0.0232 kg
Now, plug the values into the formula:
KE = (1/2)mv²
KE = (1/2)(0.0232 kg)(81.9 m/s)²
= (0.5)(0.0232 kg)(6704.61 m²/s²)
= (0.5)(0.0232 kg)(6704.61 J/kg)
= 77.8 J
Therefore, the correct answer is (a) 77.8 J.