Answer :
The maximum height the rocket would achieve without air resistance is 146.6 m, which includes an additional 24.6 m due to the energy that would not be lost to air resistance.
The student is asking about the impact of air resistance on the maximum height achieved by a model rocket. The problem originally states that the rocket reaches a height of 122 meters while overcoming a work of -880 J due to air resistance. To find the height it would have reached without air resistance, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
If there were no air resistance, the model rocket would not lose 880 J of energy. The work done by gravity is the same in both scenarios since it only depends on the mass of the rocket, the height it reaches, and gravitational acceleration. Therefore, without air resistance, that 880 J would contribute to a higher ascent. By using the relation Work = m imes g imes h, where m is the mass of the rocket, g is the acceleration due to gravity (9.81 m/s2), and h is the height, we can calculate the additional height the rocket would gain.
With the absence of air resistance, the additional height ( extbf{ extDelta h}) can be found using the expression extDelta h = Work / (m imes g). Thus, extDelta h = 880 J / (3.65 kg imes 9.81 m/s2) results in extDelta h ≈ 24.6 m. Therefore, the rocket would achieve a maximum height of 122 m + 24.6 m = 146.6 m in the absence of air resistance.
