Nivedh was right.

In the first case,

 change in velocity= final velocity vector + (-initial velocity vector).

initial velocity was towards north.

so, -initial velocity vector will be towards south

So, the resultant wil be towards south west.

GOT IT?????.

 

In the second case, the answer will be  u/cos#.

The only thing to note is that the distance between two pulleys is fixed, whereas the distance of the block, from the horizontal support is not fixed and double derivative of this length gives the acceleration of the block.