The title could be: Calculating Energy Loss and Conservation in Falling Objects

[sunaluna]

Homework Statement

So, I need a little help with a few problems
So, say a 2kg pine cone drops from a tree 41 meters high. If it hits the ground at 10m/s then how much was lost to entropy?
Or
A 1800kg roller coaster begins at the top of 190m hill, at what height will the velocity be 24m/s and what will be its kinetic energy when it reaches a height of 10m above the ground.?
Thanks for any or all help.

Homework Equations

Energy of work = Force times distance
Gravitational potential = mgy
Kinetic Energy = .5 time mass time velocity squared

The Attempt at a Solution

For the 2nd one, I used mgy= .5 time mass time velocity squared but submitted 24 for the velocity to find y but I don't think it's right.
For the 1st, I used mgy+.5 time mass time velocity squared to find the energy but don't know where to go from there.

 

[Spinnor]

Energy initial = energy final

potential energy of pine cone up in tree =

kinetic energy of pine cone before it hits + energy "lost" on the way down

You can figure out two of those to find the third.

For the second part,

Energy initial = energy at some intermediate step

potential energy up high =

potential energy up not so high + kinetic energy at that not so high place