https://www.thoughtco.com/thmb/cXZTSQkNjEIfFoxoitcB8PsZAPg=/4400x2475/smart/filters:no_upscale()/150818645-56b3c2ee5f9b5829f82c275c.jpg
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In my opinion using conservation of energy idea: E initial $=$ E final is usually the best way to think about things. To help, think through what is going on. Drawing a sketch can help to visualize, especially when dealing with energy.
To help visualize this problem:
Grab your phone. Go above your bed.
- Lift your phone rapidly [make sure your hand is moving faster upwards like when you are about to throw something] (you are applying a force upwards) for about 10 inches
-$>$ analogous to how the stone has an applied force upwards
Let go of your phone.
- What happens to the phone? It continues to go upwards into the air even though your hand no longer touching it. It reaches a maximum height.
Then comes back down ... catch it!
When you lifted your phone rapidly you were doing work on the phone. What does that mean .. you applied a force over some distance. You did work on it.
Because you did work on it, you transferred to it kinetic energy evident because it \textbf{moves} upwards (from the work energy theorem). When you let go, the phone continued to go upwards and as it reached its maximum height, its kinetic energy changed (decreasing because it went slower and slower) into potential energy (it is now vertically higher up relative to point of release).
At the maximum height the object is stationary for a split second and has 0 kinetic energy. That means at this point all of its energy is gravitational potential energy