Final answer:
A sprinter exerts a backward force on the track, resulting in a reaction force that propels them forward. To calculate the average force exerted by a 60.0-kg sprinter, energy considerations are used to account for work done against headwind and change in kinetic energy.
Step-by-step explanation:
The forward force on a sprinter can be understood using the concept of Newton's Third Law of Motion. When a sprinter pushes back hard on the track with their feet, the track exerts an equal and opposite reaction force that propels the sprinter forward. This action increases the kinetic energy of the sprinter, helping to maintain speed while racing.
For a 60.0-kg sprinter accelerating from 2.00 to 8.00 m/s over a distance of 25.0 m, we can calculate the average force exerted. Considering energy considerations, we need to calculate the work done against the headwind and the increase in kinetic energy:
- Work done against the headwind = Force × Distance = 30.0 N × 25.0 m
- Kinetic energy increase = ½ × mass × (final velocity)^2 - ½ × mass × (initial velocity)^2
To find the average force exerted by the sprinter, we combine the work done against the headwind and the change in kinetic energy and divide the total by the distance over which the force was exerted.