Final answer:
The work done by air resistance on the baseball is calculated using the work-energy principle and involves determining the change in both kinetic and potential energy as the baseball moves.
Step-by-step explanation:
The student's question is related to the work done on a baseball by air resistance during its trajectory in a baseball game. The work done by air resistance can be calculated using the work-energy principle. The initial kinetic energy (KE) of the baseball can be calculated with the formula KEi = 0.5 * m * vi2, using the mass (m) 0.25 kg and the initial velocity (vi) 40 m/s. Similarly, the final kinetic energy (KEf) can be calculated using the final velocity (vf) 30 m/s.
The change in gravitational potential energy (PE) due to the height (h) change must also be accounted for, using PE = m * g * h with gravity (g) approximated as 9.81 m/s2 and the height gain of 20 m. The work by air resistance (Wair) is then the negative change in total mechanical energy, or Wair = (KEi + PEi) - (KEf + PEf). One must remember that the initial potential energy PEi is 0 since the ball starts at the original height.