Final answer:
The height attained by the fully charged battery is approximately 4800 meters. The velocity attained utilizing the stored energy in the battery with 100% efficiency is approximately 153.3 m/s. The battery has a much higher energy content per unit mass compared to gasoline.
Step-by-step explanation:
To calculate the potential energy of the battery when fully charged, we can use the equation PE = mgh, where m is the mass of the battery, g is the acceleration due to gravity, and h is the height. Rearranging the equation, we have h = PE / (mg). Substituting the values, we get h = (5A × 24h × 3600s/h × 12V) / (30kg × 9.8m/s^2). Solving this, we find that the height attained is approximately 4800 meters.
To calculate the velocity attained by utilizing the stored energy in the battery with 100% efficiency, we can use the equation KE = 0.5mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity. Rearranging the equation, we have v = sqrt(2KE / m). Substituting the values, we get v = sqrt((5A × 24h × 3600s/h × 12V) / 30kg). Solving this, we find that the velocity attained is approximately 153.3 m/s.
To compare the energy content per unit mass between the fully charged battery and gasoline, we need to calculate the energy content per unit mass for the battery. Dividing the energy stored in the fully charged battery by its mass, we get (5A × 24h × 3600s/h × 12V) / 30kg. Comparing this with the given energy content of gasoline (4.5 x 10^7 J/kg), we can see that the battery has a much higher energy content per unit mass.