A 54.5 kg. skateboarder starts out with a speed of 1.90 m/s. He does +80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is 5.90 m/s.

(a) Calculate the change (ΔPE = PEf - PE0) in the gravitational potential energy.

initial Ke = (1/2)(54.5)(1.9)^2 = 98.4 J

final Ke = (1/2)(54.5)(5.9)^2 = 948.6 J

increase in Ke = 85.2 J

PEf + Ke f = PEi + 80 - 265 + Ke i

PEf - PEi = 80 - 265 + 98.4 - 948.6

= - 1035 J

To calculate the change in gravitational potential energy (ΔPE), we need to know the initial and final heights of the skateboarder. However, in the given information, the heights are not mentioned. Therefore, we cannot calculate the change in gravitational potential energy with the given information.