To solve this problem, you can use the equation for the conservation of energy, which states that the initial potential energy of the spring plus the work done by friction is equal to the final kinetic energy of the block.
The initial potential energy of the spring is given by 0.5kx1^2, where k is the force constant of the spring and x1 is the initial compression of the spring.
The work done by friction is equal to the force of friction times the distance over which it acts, which is given by µkmg*x1, where µk is the coefficient of kinetic friction, m is the mass of the block, g is the acceleration due to gravity, and x1 is the distance the block moves before coming to rest.
The final kinetic energy of the block is given by 0.5mv^2, where m is the mass of the block and v is the final velocity of the block.
You can set up the equation as follows:
0.5kx1^2 + µkmgx1 = 0.5m*v^2
Substituting the given values, we have:
0.5400.3^2 + µk29.810.3 = 0.52*v^2
Solving for µk, we find that:
µk = (0.5400.3^2 - 0.52v^2)/(29.810.3)
The maximum extension x2 of the spring is equal to the distance the block travels, so we can substitute x2 for v:
µk = (0.5400.3^2 - 0.52x2^2)/(29.810.3)
Substituting the value of x2, we find that:
µk = (0.5400.3^2 - 0.520.2^2)/(29.810.3)
Simplifying, we find that:
µk = 0.2
Therefore, the answer is 0.2, letter B.