Final answer:
The change in mechanical energy of the airplane system as it climbs to a cruising altitude of 2,330 meters while maintaining a speed of 95.0 m/s is 24.63 MJ.
Step-by-step explanation:
To determine the change in mechanical energy of the system as the plane climbs to a cruising altitude of 2,330 meters while maintaining a constant speed of 95.0 m/s, we consider both the potential and kinetic energy changes of the airplane.
The change in kinetic energy (ΔKE) can be calculated using the formula ΔKE = ½ mv², where 'm' is the mass of the airplane and 'v' is its velocity. The initial kinetic energy is zero since the plane starts at rest, so the final kinetic energy when the plane reaches the cruising speed is:
ΔKE = ½ * 900 kg * (95.0 m/s)² = 4,068,750 J
The change in potential energy (ΔPE) due to the change in height can be calculated using ΔPE = mgh, where 'g' is the acceleration due to gravity (9.81 m/s²), and 'h' is the altitude change. So:
ΔPE = 900 kg * 9.81 m/s² * 2,330 m = 20,558,700 J
The total change in mechanical energy (E) is the sum of the changes in kinetic and potential energy:
E = ΔKE + ΔPE = 4,068,750 J + 20,558,700 J = 24,627,450 J
Converting this into megajoules (MJ), we divide by 1,000,000:
E = 24.63 MJ