# Potential/kinetic/mechanical energy

1. Nov 4, 2015

### J827

1. The problem statement, all variables and given/known data
A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40J. At the exact top of its trajectory, its total mechanical energy is 140J. To what vertical height above the ground does it rise, assuming no air resistance?

2a. Relevant equations
gravitational potential energy = mgh
potential + kinetic = mechanical energy

3a. The attempt at a solution
if the rocket has 40J of energy on the ground, it has gained 100J at the top of its trajectory*.
GPE = 100J
GPE = mgh
100 = (10)h
h = 10 meters

*I think this is true, but I can't explain why. It's not like it lost 40J of energy to reach the top, but if it's at the top, it isn't moving anymore, so the final kinetic energy is zero, yes?

also, is there a way to use kinematic equations to solve this problem? here's what I tried:
2b. Relevant equations
gravitational potential energy = mgh
potential + kinetic = mechanical energy
kinetic energy = 1/2mv^2
weight = mass * gravity

3b. The attempt at a solution
10N = m(10); m = 1kg
initial kinetic energy = 40J
40 = 1/2 m v^2; initial v^2 = 80
final velocity = 0
0 = 80 + 2(-10)d
d = 4 meters

I feel like I'm missing something fairly obvious. Thanks for any light you can shed.

2. Nov 4, 2015

### Henryk

Yes, you are missing something obvious. It is a toy rocket, toy engines are working for a while ....
Let me know if you need more hints

3. Nov 4, 2015

### SammyS

Staff Emeritus
Yes, you are missing something.

The rocket goes straight up. At the top of its trajectory, what is its speed? Is it zero? If so, what is its kinetic energy at that instant?

4. Nov 5, 2015

### J827

I'm sorry....I don't know what you're trying to hint at here. Are you trying to say that the kinetic energy is still 40 at the top because of the engine? That doesn't make any sense, and is in direct conflict with this:

I said that before. The speed at the top is zero, so kinetic energy should be zero. That would make the 140J all potential, resulting in an answer of 14 meters.

I have been told that the answer to the problem is 10 meters, but I don't understand how the GPE is only 100J. energy isn't a vector quantity, so can't be a negative value....

5. Nov 5, 2015

### Henryk

The rocket is launched straight up. That means no horizontal velocity and we can assume that it moves straight up.
At the top, the velocity is zero, therefore, kinetic energy is zero and all energy is potential.
Therefore, the height is 140 J/10 N = 14 m.

6. Nov 5, 2015

### haruspex

By a usually reliable source?
Everyone here seems to agree it's 14m.

7. Nov 5, 2015

### J827

yeah....the answer key. however, just because it's usually reliable doesn't mean it's infallible. however, this one seems to have been perpetuated for a long time.... through Google, I found this problem on several websites, and the answer given almost every time was 10 m. The only site where I found a handwritten solution gave the answer as 14 m. Gets to the point where it's really better to talk to real people, you know? Thanks for the help.

8. Nov 5, 2015

### haruspex

Looks like the question and answer have been blindly copied around from some common erroneous source.