50 points!
consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. it falls to the ground. think about the amounts of potential and kinetic energy the bowling ball has:
• as sits on top of a building that is 40 meters tall.
• as it is half way through a fall off a building that is 40 meters tall and travelling 19.8 meters per second.
• as it is just about to hit the ground from a fall off a building that is 40 meters tall and traveling 28 meters per second.

1. does the bowling ball have more potential energy or kinetic energy as it sit on top of the building? why?
2. does the bowling ball have more potential energy or kinetic energy as it is half way through its fall? why?
3. does the bowling ball have more potential energy or kinetic energy just before it hits the ground? why?
4. what is the potential energy of the bowling ball as it sits on top of the building?
5. what is the potential energy of the ball as it is half way through the fall, 20 meters high?
6. what is the kinetic energy of the ball as it is half way through the fall?
7. what is the kinetic energy of the ball just before it hits the ground?

Every object has a total energy which is the sum of its kinetic and potential energy:

E = Ek + Ep

Kinetic energy is, as the name suggests, the energy of moving. It is given through the equation:

Ek = m • v^2 / 2

From here, we can see that Ek depends on the object's velocity; if v=0, then Ek will also be zero.

Potential energy is the energy an object has on a certain height:

Ep = m • g • h

Obviously, if the height is zero, then the Ep=0 too.

Another important thing to note is that E is always constant; if Ek increases (or decreases), Ep will decrease (or increase) so that their sum will always be a constant value.

If the bowling ball sits at the top of the 40 meters tall building, it has no velocity, it doesn't move, but it is located on a certain height.  

That means that, at the top of the building, the bowling ball has no kinetic energy:

E = Ep + Ek

- no velocity ---> Ek =0

E = Ep = mgh

Ep = 2 kg • 9.81 m/s^2 • 40 m

E = Ep = approximately 785 J

To conclude, at the top of the building Ep > Ek.

Now, the ball is falling, and it's halfway down and it's travelling 19.8 m/s. Now, its kinetic energy is:

Ek = m • v^2 / 2

Ek = 2 • 19.8^2 / 2

Ek = approximately 392 J

Now, since the ball is halfway down, that means that its height is 20 meters. So, its Ep is:

Ep = mgh

Ep = 2•9.81•20

We already stated that total energy is constant and that is the sum of Ep and Ek and that it is around 785 J. We could also find Ep:

Ep = E - Ek

Ep = 785 - 392

Whichever way we use to calculate, we'll get the value of approximately 392 J.

That means that, halfway down, Ep=Ek.

Since the ball is halfway down, that means that its Ep is half the value it was while at the top of the building. The other half is used on the ball's velocity producing kinetic energy. That's why these two are equal at the halfway down.

Just before it hits the ground, the bowling ball has no height, meaning it has no potential energy. That also means that its total energy is equal to its kinetic energy:

E = Ep + Ek

Ep = 0

E = Ek

We already said that the ball's total energy was around 785J, so its kinetic energy just before it hits the ground will be that exact value.

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