A55.6-kg skateboarder starts out with a speed of 2.44 m/s. he does 80.4 j of work on himself by pushing with his feet against the ground. in addition, friction does -244 j of work on him. in both cases, the forces doing the work are non-conservative. the final speed of the skateboarder is 7.24 m/s. (a) calculate the change (pef - pe0) in the gravitational potential energy. (b) how much has the vertical height of the skater changed? give the absolute value.

(a) -1620.8 J

The initial kinetic energy of the  skateboarder is:

where m is the skateboarder's mass and u his initial speed;

While the final kinetic energy is

where v is his final speed.

So the change in kinetic energy is

According to the work-energy theorem, the change in mechanical energy (kinetic+potential) of the skateboarder is equal to the work done on it:

where

is the work done by the skateboarder on himself

is the work done by friction

is the change in gravitational potential energy

Solving for ,

(b) 2.97 m

The change in potential energy of the skateboarder can be written as

where

m = 55.6 kg is the mass

g = 9.8 m/s^2 is the acceleration of gravity

is the change in vertical height of the skateboarder

Solving for ,

Where the negative sign means the skateboarder has moved downwards. Since we are interested only in the absolute value, the answer is

h = 2.97 m

d. air pressure decreases as altitude increases.