Physics troubles?

Question

A 54.0 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 6.15 m/s.
(a) Calculate the change (PE = PEf - PE0) in the gravitational potential energy.
J

(b) How much has the vertical height of the skater changed?
m

(c) Is the skater above or below the starting point?
below the starting point
above the starting point


Really having a hard time doing this problem, gravitational potential energy problem no examples like this in my book and the teacher never taught us this part of the chapter can you please help me get started!

comparing the final kinetic energy to the starting and energy gains and losses:
1021.2075=97.41-185+delta PE
delta PE=1108.8 J
this response was incorrect according to my teacher and I do not know why because all of your work looks right.....any suggestions

Answer 1

All of this can be modeled using energy
Set the starting height as the zero potential energy point. The starting kinetic energy of the skater
.5*m*vi^2
=.5*54*1.9^2
=97.47 J

Next look at the energy added by his feet and lost due to friction
80-265
-185 J

The skater also has a final kinetic energy of
.5*54*6.15^2

=1021.2075 J

comparing the final kinetic energy to the starting and energy gains and losses:
1021.2075=97.41-185+delta PE
delta PE=1108.8 J

In order for the skater to gain kinetic energy given the loss due to friction and small added by pushing the skater has descended some height. It wasn't asked for, but I'll compute it:

1108.8=m*g*h
using g=9.81
h=1108.8/(54*9.81)
about 2.1 meters

j