Question

Using energy considerations, calculate the average force (in N) a 67.0 kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 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.

Answer 1

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

`F_(sprinter)=110.4N`

Step-by-step 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

`W=F_(total).d`

So

`W=1/2mv_(f)^2-1/2mv_(i)^2\\F_(total)=(1/2mv_(f)^2-1/2mv_(i)^2)/(d) \\F_(total)=(1/2(67.0kg)(8.00m/s)^2-1/2(67.0kg)(2.00m/s)^2)/(25.0m) \\F_(total)=80.4N`

and we know that the force the sprinter exerted Fsprinter the force of the headwind Fwind=30.0N

So

`F_(sprinter)=F_(total)+F_(wind)\\F_(sprinter)=80.4N+30N\\F_(sprinter)=110.4N`