The coefficient of friction is 0.051
Explanation:
The motion of the skater is a uniformly accelerated motion, therefore we can use the following suvat equation:

where:
v = 0 is the final velocity of the skater (he comes to a stop)
u = 10.0 m/s is his initial velocity
a is the acceleration
is the distance he travels before stopping
Solving for a, we find the acceleration of the skater:

We also know that the net force acting on the skater is the force of friction, therefore we can write (Newton's second law of motion):

where
is the force of friction
m is the mass of the skater
is the coefficient of friction
is the acceleration
is the acceleration of gravity
Solving for
, we find the coefficient of friction:

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