Final answer:
To calculate the average horizontal force exerted during acceleration, we use Newton's second law and kinematic equations to first find the acceleration during the first 41 meters, then calculate the force using the sprinter's mass and this acceleration.
Step-by-step explanation:
The question involves calculating the average horizontal component of force exerted on the sprinter's feet by the ground during acceleration. To find this, we first note that the sprinter's mass is 69 kg and that the acceleration is uniform over the first 41 meters.
Using Newton's second law, F = ma, we look for the acceleration 'a' by first calculating the final velocity at the end of the acceleration phase using the formula v^2 = u^2 + 2as, where 'u' is the initial velocity (0 m/s), 'v' is the final velocity, 'a' is the acceleration, and 's' is the distance (41 m).
Once 'v' is known, since the sprinter maintains this speed for the remaining distance, we can use the total time of 10 seconds to find the time spent accelerating. Subtracting the time spent at constant speed from the total time gives us the time spent accelerating. Knowing the acceleration time and final velocity, we can return to Newton's second law to solve for the force 'F' by rearranging the equation to F = m * a. We conclude that the force exerted is the product of the sprinter's mass and the calculated acceleration.