Using energy considerations, calculate the average force (in N) a 70.0 kg sprinter exerts backward on the track to accelerate from 2.00 to 9.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him.

137.8 N

Explanation:

First we need to find the acceleration of the sprinter. To do so, we can use the Torricelli's equation:

V^2 = Vo^2 + 2*a*S

9^2 = 2^2 + 2*a*25

81 = 4 + 50a

50a = 77

a = 77/50 = 1.54 m/s2

Now, to find the resulting force in the sprinter, we can use the following equation:

Force = mass * acceleration

Force = 70 * 1.54 = 107.8 N

If we have a 30 N force against the sprinter, the total force applied is:

Resulting force = Applied force - Wind force

107.8 = Applied force - 30

Applied force = 137.8 N