Final answer:
The kinetic energy of a 90,000-ton aircraft carrier moving at 30 knots is estimated using conversions to the Metric system and the kinetic energy formula. The calculated value is approximately 9.722 × 10^11 J, with the closest provided option being 5.4 × 10^11 J (option b), despite a notable discrepancy.
Step-by-step explanation:
To estimate the kinetic energy of a 90,000-ton aircraft carrier moving at 30 knots, we must first convert the units to the Metric system. One knot is equal to 1 nautical mile per hour, and there are about 1.151 miles in a nautical mile, so 30 knots is roughly 34.5 miles per hour (mph). Converting mph to meters per second (m/s), we get that 1 mph is approximately 0.447 m/s, so 34.5 mph is about 15.42 m/s.
Next, we convert the mass of the aircraft carrier from tons to kilograms. Since 1 ton is equivalent to 2,000 pounds, and there are 0.453592 kilograms per pound, a 90,000-ton carrier is 90,000 * 2,000 * 0.453592 kilograms, or approximately 81,646,560 kilograms.
Now, we can calculate the kinetic energy (KE) using the formula KE = (1/2) * mass * velocity^2. Plugging in our values, we get KE = (1/2) * 81,646,560 kg * (15.42 m/s)^2, which equals 9.722 × 10^9 kg * m^2/s^2. Since 1 joule is 1 kg * m^2/s^2, the kinetic energy is about 9.722 × 10^9 joules or 9.722 × 10^11 joules.
Comparing our calculated value to the options given, we see that the closest estimate is option b) 5.4 × 10^11 J. However, our calculated value is significantly different from any of the options, suggesting a possible error in our calculations or the provided options. Nonetheless, based on the given options and standard conversion factors, we would choose option b as the closest estimate to the calculated kinetic energy of the aircraft carrier.