Final answer:
The work done by air resistance on the motorcyclist can be found by calculating the difference in mechanical energy from the initial to the final state. After performing the calculations, the work by air resistance is found to be -7500 J, which means option C) -7500 J is correct.
Step-by-step explanation:
To determine the work done by air resistance, we must first analyze the change in mechanical energy of the motorcyclist as he goes from the higher to the lower cliff. Mechanical energy consists of kinetic and potential energy; in this problem, both will change due to the motion and elevation change.
We can use the conservation of mechanical energy formula to calculate the initial and final mechanical energy, provided air resistance has done work on the system:
MEi = KEi + PEi
MEf = KEf + PEf
The work done by air resistance (Wair) is the difference between the initial and final mechanical energy:
Wair = MEf - MEi
Calculating the individual energies:
KEi = (1/2) * m * vi2 = (1/2) * 125 kg * (30 m/s)2
PEi = m * g * hi = 125 kg * 9.81 m/s2 * 20 m
KEf = (1/2) * m * vf2 = (1/2) * 125 kg * (22 m/s)2
PEf = m * g * hf = 125 kg * 9.81 m/s2 * 10 m
Then, we now solve for Wair given the mechanical energy values:
Wair = [(1/2) * 125 kg * (22 m/s)2 + 125 kg * 9.81 m/s2 * 10 m] - [(1/2) * 125 kg * (30 m/s)2 + 125 kg * 9.81 m/s2 * 20 m]
After calculation, Wair will be found as -7500 J, indicating that air resistance has done negative work on the system (opposed the motion), taking away energy.