Assumptions: Kinetic Energy=KE, Potential Energy=PE
m=mass of the skateboarder=55 kg, Velocity v=1.80m/s
So ,Initial Energy(KE) of the skateboarder=mv^{2}/2 = 0.5* 55 * (1.8)^2 = 89.1 J
Now from law of conservation of energy we can write that
Work Done by the man/boy
=(Change in KE)+(Change in PE)+(Friction)
=(KE final-KE initial)+(PE final- PE initial)+(Friction)
= (KE final-KE initial)+ ?PE +(Friction)---------------------(1)
Now (PE final-PE initial) is to be determined.
But PE initial=0
So (PE final- PE initial)=?PE=PE final
And KE final= mv^{2}/2=.5*55*(6)^2=990 J
KE initial=89.1 J(already determined)
So (KE final-KE initial)= 900.9 J
Work done by the man=80 J, Friction=-265 J
Now from equation (1) we get
80=900.9+?PE-265
?PE=-1085.9 J
=-1.09KJ(approx)
This -ve sign indicates that the skateboarder losses some vertical height.
Part 2:
Change in potential energy
=?PE
=m*g*h(m=mass, g=gravitational force, h=height)
So -1.09KJ=55*9.8*h
h= -1085.9/(55*9.8)
=-2.02m or 2.02 m below the starting point