To solve this problem we will apply the concept related to the kinetic energy theorem. Said theorem states that the work done by the net force (sum of all forces) applied to a particle is equal to the change experienced by the kinetic energy of that particle. This is:
[tex]\Delta W = \Delta KE[/tex]
[tex]\Delta W = \frac{1}{2} mv^2[/tex]
Here,
m = mass
v = Velocity
Our values are given as,
[tex]m = 79.7kg[/tex]
[tex]v = 4.77m/s[/tex]
Replacing,
[tex]\Delta W = \frac{1}{2} (79.7kg)(4.77m/s)^2[/tex]
[tex]\Delta W = 907J[/tex]
Therefore the mechanical energy lost due to friction acting on the runner is 907J
