A quick calculation study

I just saw this on youtube:

Here is some analysis on it (please do puzzle first):

this was helpful.  It shows how thinking out the move as simple as this leads to victory or defeat (or draw).  Much of my trouble, even with a lead, happens during the endgame (when I don't have to worry about losing on time).

so often we beginners are too eager to get out of check and forget to calculate how the move will affect all pieces.

To stop the pawn, Black needs to do one of two things:

A) Capture the pawn or get to d5 or e5 before it moves.

B) Capture the pawn or get to d6 or f6 when it reaches e7.

Knowing those goals of Black, it's easy to see what works and what doesn't.

1 Kf1 allows Ng3+/Nf5.

1 Kf2 allows Nc3/Ne4+/Nd6 or Nf6. 

1 Kg2 allows Nf4+/Nxe6.

1 Kh1 allows Ng3+/Nf5.

1 Kh2 wins.  Black can't reach the springboard square of g2 in two moves, and the other springboard square of e4 won't give check.