Gravitational potential, highest point, and final velocity

AI Thread Summary
The discussion revolves around the mechanics of a model rocket, focusing on its energy transformations during flight. The mechanical energy at 220 m is calculated to be 4.73 x 10^4 J, while gravitational potential energy at the highest point is debated, with one participant suggesting it could be 4.08 x 10^4 J. The height at the highest point is estimated to be 1.39 x 10^3 m, derived from energy conservation principles. The conversation emphasizes that once the rocket's fuel is depleted, its energy transitions from kinetic to potential energy until it reaches the peak. The final velocity upon hitting the ground is discussed in terms of kinetic energy maximization just before impact.
x3lifelove
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A model rocket has a mass of 3.00kg. It is fired so that when it is 220 m above the ground it is traveling vertically at 165m/s. At the point its fuel runs out so that the rest of the flight is without power. Assume that the effect of air friction is negligible and that all potential energies are measured from the ground.
A) What is the mechanical energy of the rocket when it is 220 m above the ground? (I figured this one out and got 4.73 x 10^4 J
B) When it reaches the highest point on its trajectory, what will its gravitational potential energy be?
C)How far above the ground is the rocket at its highest point?
D)When it hits the ground, what is its velocity?

A) I got the answer correct
B) i got a answer of 3.24 x 10^3 J but I'm unsure if I am correct or not.
C) I honestly have no clue.
D) I'm unsure as well.
If you even could help me figure out how to start B-D that would be really appreciated, i would most likely be able to figure out the actual answer on my own.
 
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Once the rocket fuel has run out, what could happen to change the rocket's energy?

What is the significance of the highest point of the flight (which is what C asks about) in terms of energy (which is what the problem is focusing on)?
 
Modulated said:
Once the rocket fuel has run out, what could happen to change the rocket's energy?

What is the significance of the highest point of the flight (which is what C asks about) in terms of energy (which is what the problem is focusing on)?

The rocket energy would be converted back to potential energy before falling to earth. Since its a system without any external forces its isolated. So that would be the Ek=Ep ?
So then the answer to B) would be 4.08 x 10^4J ?

Then for C would be 1.39 x 10^3m .
 
x3lifelove said:
Since its a system without any external forces

Do you really mean this?

its isolated.

This isn't quite what you mean either, but it's getting closer. Can you rephrase what you mean by "isolated"?

Stop giving answers in numbers - work out what's going on first, and then you can do the arithmetic. And think about the answer to my second question (from the previous post).
 
For B and C:

PE = mass * gravitational acceleration * height

The only problems here is that you have to solve for the height. That seems straightforward enough.

For height use the equation v(f)^2 = v(i)^2 + 2ad

Obviously vertical velocity at the top of the trajectory (where PE is maximum) will be 0, so plug in 0 for v(f). V(i) is 165 m/s as given, a should be known as well (a=g). D, or displacement, is what we're looking for.

Looking past the mathematics, the PE at the top of the trajectory should be equal to the ME you found, since it is an isolated system. At the top, PE = max and KE = 0. ME = PE + KE.

[PLAIN]http://i.min.us/isjF6.jpg
 
Last edited by a moderator:
For D:

As the rocket approaches the bottom of its trajectory, KE will reach its maximum and PE will be 0 for an instant.


[PLAIN]http://i.min.us/icCREI.jpg

[PLAIN]http://i.min.us/ic8ByI.jpg
 
Last edited by a moderator:
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