Final answer:
To calculate the average force exerted by the sprinter, you need to consider the relationship between work and energy. The average force exerted by the sprinter is 30.0 N.
Step-by-step explanation:
To calculate the average force exerted by the sprinter, we need to consider the relationship between work and energy. The work done by the sprinter to accelerate from 2.00 to 8.00 m/s can be found using the work-energy theorem:
Work = Change in kinetic energy
Since the sprinter is exerting a backward force, the work done by the sprinter is negative because the force and displacement are in opposite directions. Therefore:
Work = -Force x Displacement
Using the given values, we can calculate the work done by the headwind:
Work done by headwind = -30.0 N x 25.0 m = -750 J
Now, we can equate the work done by the sprinter to the work done by the headwind:
Work done by sprinter = -Force x 25.0 m
Since the sprinter's mass is 60.0 kg and the initial and final velocities are given, we can use the kinetic energy formula to calculate the initial and final kinetic energies and find the change in kinetic energy:
Initial kinetic energy = (1/2) x mass x (initial velocity)^2
Final kinetic energy = (1/2) x mass x (final velocity)^2
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Finally, we can substitute the change in kinetic energy and the work done by the headwind into the equation:
Change in kinetic energy = -Force x 25.0 m
Solving for the force, we find:
Average force = (-Work done by headwind) / 25.0 m
Plugging in the values, we get:
Average force = 750 J / 25.0 m = 30.0 N