Final answer:
The work done by air resistance can be found using the work-energy principle. The work done by air resistance is equal to the change in mechanical energy of the baseball. Since the baseball returns to the ground with a lower speed, it loses some of its mechanical energy, which is equal to the work done by air resistance. Therefore, the work done by air resistance is 135 J.
Step-by-step explanation:
The work done by air resistance can be found using the work-energy principle. The work done by air resistance is equal to the change in mechanical energy of the baseball. Mechanical energy is the sum of the kinetic energy and the potential energy of the baseball. Since the baseball returns to the ground with a lower speed, it loses some of its mechanical energy, which is equal to the work done by air resistance.
The change in kinetic energy can be calculated using the formula:
ΔKE = 0.5 * m * (v_final^2 - v_initial^2)
where ΔKE is the change in kinetic energy, m is the mass of the baseball, v_final is the final speed of the baseball, and v_initial is the initial speed of the baseball.
Plugging in the given values:
ΔKE = 0.5 * 0.25 kg * (27 m/s)^2 - (30 m/s)^2
ΔKE = 0.5 * 0.25 kg * 729 m^2/s^2 - 900 m^2/s^2
ΔKE = 90 J - 225 J
ΔKE = -135 J
The negative sign indicates that the kinetic energy is decreasing, which means the work done by air resistance is positive. Therefore, the work done by air resistance is 135 J.