Relationship between Kinetic Energy and Gravitational Potential Energy.

[Craptola]

Hello, having had an interest in physics for a while I recently enrolled on an access to higher education course to study it. Unfortunately I seem to have fallen at the first hurdle. First off I'd like to apologise profoundly and profusely for the simple problem you are about to read, but I have litterally just started the course and don't know much. So today I went to my first lecture, I thought it was going well and I fully understood everything that was being said but then came the homework, I was given the following problem and am strugling to understand where I was going wrong.

Homework Statement

g=9.81
A ball of mass 0.5 kg was thrown directly upwards at a speed of 6.0m/s Calculate:
A) Its kinetic energy.
B) Its maximum gain of potential energy.
C) Its maximum height gain.

Homework Equations

A) KE = 1/2mv^2
B) (assumption) Conservation of energy laws.
C) (assumption) GPE = mgh

The Attempt at a Solution

A) Easy enough KE=1/2mv^2 Giving me 0.5 x 0.5 x 36 = 9J

B) The only formula I'd been given in the class or on any of the handouts for Gravitational potential energy was GPE = mgh, seeing as I (as far as I'm aware) cannot determine the height from the given values it must have something to do with the conservation of energy law. Since there was no stated air resistance I have to assume that it is negligable and therefore when the ball reaches its peak and the loss of kinetic energy is 9J the gain in potential energy must also be 9J.

C) Here I figured that I could calculate the height by rearranging GPE = mgh to
h = GPE/mg (I'm not sure if this is the correct way to rearrange this formula, this may be my mistake) the resultant equation gives me an irrational number (rounded to 1.84).

Once again I apologise for the very simple problem I'm having but I can't really see where I've gone wrong. Any help with this would be greatly appreciated.

 

[danielakkerma]

Hi..
The answer is well poised within your first, solved, query;
All of the energy the ball has, is its initial Kinetic energy, granted to it by the throw; that's all!
Since the gravitational field is conservative, the ball doesn't gain anything and(assuming there's no air resistance) doesn't lose any of it in flight...
So you have your answer!
Daniel
P.S
You can also compute the height kinematically, by using {v_f}^2 = {v_0}^2-2gh, where v_f =0, and v_0 is your initial velocity; Verify your energy considerations with that...
And you haven't gone wrong...!