(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