7.48. a)
This problem involves repeated applications of the conservation of energy theory. Namely,
If we consider the initial condition when the block first comes into contact with the spring and the final when the spring is fully compressed a distance d, we get the following.
Plugging our values for 
, k, 
, and m, and using the
quadratic formula to solve for d, we find
d = .378 m
b)
Now, we are looking for the velocity when the spring is again unstretched. This time, consider the initial energy again when the block first makes contact with the spring and the final when the spring is in its unstretched position. The distance travelled is now 2d. So, our equation becomes
again, the only unknown in this equation is the velocity v. Solving for it yields
v = 2.30 m/s
c)
Now, we want the distance that the block travels after it leaves the spring. Call it D. This time, take the same initial energy as before, all of this energy is converted into work done by friction.
Solving for D yields
D = 1.08 m