Calculate Maximum Velocity of Girl on Swing

[PeterO]

oh! well then you'd think that technically there still is a potential energy at the lowest point, since it's 1 meter above ground, which means v=sqrt2ghfinal - sqrt2ghinitial, but that's incorrect, because it violates the law of conservation of energy. but hm...maybe h=2meters, because it's 2 meters from the ground. I'm really sorry if you are confused. I am too!

This problem has little to do with the actual Potential energy, and everything to do with the CHANGE in Potential energy.
In all problems, we get to set where zero height is, and invariably we choose either the lowest point, the highest point, the starting point or the finishing point.

For example

Lowest point - A swing or similar

Highest point - a satellite [rare]

Start point - projectile motion

Finish Point - roller coaster.

 

[PeterO]

the height is the y direction between the heighest point and the lowest point. does that make sense?

On in proper description: The h value [change in height] is the difference between highest point and lowest point.