In: Physics
Ist line of your question is a mismatch, "with an initial velocity of 13 m/s starting from rest" In my solution, I have considered initial velocity 13 m/s and final zero, try to understand the technique to solve and solve accordingly.
Final value of the kinetic coefficient of friction I got is highly impractical as well as for such values the block will not move, so if your data are as per my consideration then the kinetic coefficient must be zero since the body will not move. But if data are different you can follow the above procedure to get the result.
Note: for coefficient of friction greater than or equal to tan theta body will note move