Answer:
[tex]F_{sprinter}=110.4N[/tex]
Explanation:
Given data
Mass m=67.0 kg
Final Speed vf=8.00 m/s
Initial Speed vi=2.00 m/s
Distance d=25.0 m
Force F=30.0 N
From work-energy theorem we know that the work done equals the change in kinetic energy
W=ΔK=Kf-Ki=1/2mvf²-1/2mvi²
And
[tex]W=F_{total}.d[/tex]
So
[tex]W=1/2mv_{f}^2-1/2mv_{i}^2\\F_{total}=\frac{1/2mv_{f}^2-1/2mv_{i}^2}{d} \\F_{total}=\frac{1/2(67.0kg)(8.00m/s)^2-1/2(67.0kg)(2.00m/s)^2}{25.0m} \\F_{total}=80.4N[/tex]
and we know that the force the sprinter exerted Fsprinter the force of the headwind Fwind=30.0N
So
[tex]F_{sprinter}=F_{total}+F_{wind}\\F_{sprinter}=80.4N+30N\\F_{sprinter}=110.4N[/tex]
