Questions on conservation of energy

[Kalix]

Homework Statement

Question: An airplane is 250m from the zero heigh and drops a package:

a. What is the objects kinetic energy if the velocity is moving at 10m/s. How much energy is left? What height should the object be at?

b. What is the objects kinetic energy if the velocity is 30m/s? How much energy is left? What height should the object be at?

Homework Equations

KE=.5mv^2
PE=mgh
mgh(initial)+mv(initial)^2=mgh(final)+.5mv(final)^2 (I am not sure if this equation is relevant but it might be so I thought I put it down)

The Attempt at a Solution

a. KE=.5(75)(10^2)=3750 J
I have no idea how to find how much energy is left. Is there an equation for this/
h=3750/75x9.81=5.1m

b. KE=.5(75)(30^2)=33750 J
Again I don't know how to find the amount of energy left over.
h=33750/75x9.81=5.1m

Also I don't understand what the 250m is there for but I guess it may have something to do with the amount of energy left.

 

[Doc Al]

Also I don't understand what the 250m is there for but I guess it may have something to do with the amount of energy left.

Are we to assume that the package (and the plane that drops it) has an initial speed of zero?

If so, what's the total energy? You have the formula.

 

[Kalix]

Yes we can assume that the initial speed is zero when the package is dropped from the plane. I actually don't know how to find total energy. I don't see the equation on the equation sheet that my teacher gave us. It seems likely that TE might equal KE + PE but I really don't know for sure. Also in this particular problem are PE and KE equal to each other?

 

[Doc Al]

It seems likely that TE might equal KE + PE but I really don't know for sure.

Yes, that's conservation of energy--what you need to solve this problem.

Also in this particular problem are PE and KE equal to each other?

No. Why would you think that?

As the object falls, one form of energy increases while the other decreases.

 

[Kalix]

We did a similar problem to this in class and KE was equal to PE so I thought it might be the same case.

So this means that the height I found in parts a and b wasn't correct because I used KE as the PE value in the equation PE=mgh?

 

[Doc Al]

So this means that the height I found in parts a and b wasn't correct because I used KE as the PE value in the equation PE=mgh?

Yes, that was not correct. Instead, use the third equation you listed.

 

[Kalix]

So when I use the conservation of ME equation I am solving for the final height correct? But what equation do I use to find the energy left over. If I have KE what do I subtract from that to see what is left?

 

[iRaid]

You need to find the potential energy and subtract the kinetic energy to get what is left over

 

[Doc Al]

So when I use the conservation of ME equation I am solving for the final height correct? But what equation do I use to find the energy left over. If I have KE what do I subtract from that to see what is left?

You have the initial and final KEs and the initial PE. Solve for the final PE.

 

[iRaid]

You have the initial and final KEs and the initial PE. Solve for the final PE.

Oh yeah I see what you're saying, OP -you should do this.