Total height of the gymnast just before falling back down is=(2+.3)=2.3m
Energy gained at that point
= m*g*h(m=mass, g=gravitational force, h=height)
=55*9.8*2.3=1239.7 J
And the work done by the average force(let the force be F) that is exerted by the mat, moving through a distance of 0.3m=F*0.3 m
So, F*0.3 =1239.7 J