yeah Jump is one of the things left to do.
In the first vid I did jumping by an initial impulse and then adding gravity->multiplicating frametime aso.
That was ugly, as frametime changes HULK jumps on the moon XD
In the 2. vid theres a max humpheight - also ugly 
I always find real world physics work best, no matter how simple you want to keep things.
What I like to do for jumping in my platformers (if your interested):
-Set a 'Trajectory' value for jumping - I use a 2D vector for this.
-Set an 'Air State' and 'Ground State' for the character. This controls whether the character is in the air or not.
-When a jump action occurs, apply a large value to the characters Trajectory.y (the higher the number the highter the character will jump), then Set the characters State to Air State.
-In the characters update check if the character is in the Air state, if they are, compute the characters new Trajectory. my normal formula is 9.82m/s^2, which ends up as Trajectory.y += time_passed * gravity; time_passed is the time since my last frame.
-Then update the characters position based on the trajectory. Location.y += Trajectory.y * time_passed;
- Once the character collides with the ground, simply set the state back to ground and reset the Trajectory.y back to 0.
This is basically all I ever do and it always turns out great for me. Hope it can help you.
Quick Edit: I should mention that the initial Trajectory.Y would be a negative value (like -200) in this case.
