I gotcha
Split the question up into 3 parts.
Part 1: The dart is going through the tube.
Part 2: The dart is moving and collides with the block.
Part 3: The dart and block system move together
For part 1:
Recall the formula of Work done and write it out for this question which is trivial:
Part 2:
For this part remember it is an
inelastic collision between the dart and the block which means
momentum is conserved but energy isn't. Using this you can find out an expression for the start/initial velocity of the dart & block system as it begins to move.
Part3:
Now for this part you get an expression for the friction force being:
Now again recall the formula for Work done and
find an expression for D in terms of m,v,u_k and g.
Finally take a look at
part 1 again and
substitute appropriately into the expression you obtain in part 3 for D and that gives you the final answer!