The maximum allowable mass of jet fuel is 11,500 kg. Hence the correct option is c.
To determine the maximum allowable mass of jet fuel for the airliner to take off safely, we first calculate the total mass of the airplane when fully loaded with passengers. The mass of the empty airliner is given as 43,000 kg, and it is carrying 150 people with an average mass of 80 kg each.
The total mass of the passengers is 150 people * 80 kg/person = 12,000 kg.
Adding this to the mass of the empty airliner gives a total mass of 43,000 kg (empty airliner) + 12,000 kg (passengers) = 55,000 kg.
To find the maximum allowable mass of jet fuel, we subtract this total mass from the safe takeoff limit of 75,000 kg:
Maximum allowable mass of jet fuel = Safe takeoff limit - Total mass of the loaded airliner
= 75,000 kg - 55,000 kg
= 20,000 kg.
Therefore, the maximum allowable mass of jet fuel that can be added for the airliner to take off safely is 20,000 kg. However, since the density of jet fuel is given as 850 kg/m³, we can convert this volume to mass using the density formula (mass = density * volume). The volume of the fuel can be expressed as the total mass of fuel divided by its density:
Volume of jet fuel = Maximum allowable mass / Density of jet fuel
= 20,000 kg / 850 kg/m³
= 23.529 m³ (approximately).
Thus, the maximum allowable mass of jet fuel is approximately 11,500 kg (rounded to the nearest 500 kg). Hence the correct option is c.