Final answer:
The work done by air resistance when an object falls and lands with a certain velocity is calculated using energy conservation, considering the difference between the initial potential energy and the final kinetic energy.
Step-by-step explanation:
The question asks about the work done by air resistance when an object falls through a distance and reaches the ground with a certain velocity. To calculate the work done by air resistance on the falling mouse, we can use the energy conservation principle. The mouse has a potential energy (PE) of mgh at the start and kinetic energy (KE) of 1/2 mv² just before hitting the ground. Air resistance does work on the mouse, reducing its mechanical energy.
Using the given values, the mouse's initial potential energy is PE = mgh = (0.2 kg)(9.80 m/s²)(100 m), and its final kinetic energy is KE = 1/2 mv² = 1/2 (0.2 kg)(8.0 m/s)². The difference between the initial potential energy and the final kinetic energy gives us the work done by air resistance, i.e., Work by air = PE - KE. The assumption of no other forces, apart from gravity and air resistance, implies that all the lost potential energy has been transformed into work done by air resistance and kinetic energy.