I think I've found the answer. If dx is the change in the position of the body, then dx=-dh, so dh/dt=-dx/dt=-v, right? Another way I thought about it would be. Let A be a point such that h=AB, where B it's at ground level. Let O an arbitrary point in space, that it's on the direction of AB...
Homework Statement
Prove that the enrgy of a falling body remains constat using the derivate of a function
Homework Equations
We need to prove that:
\frac{mv^2}{2} + mgh is constant, trhat is its derivate equals 0
The Attempt at a Solution
Let the positive direction be...
First, I noticed a subtle "symmetry" in the equation, I don't know how to call it otherwise. So I plugged -y instead of y and I got the system:
af(x+y) + bf(x-y) = cf(x) +dy
af(x-y) + bf(x+y) = cf(x) - dy
Then, I played a little with the system. I won't post the whole the whole steps...
Homework Statement
Let a.b,c,d be real numbers such that a ≠ b and c ≠ 0 , find f:R->R for which this statement holds:
af(x+y) + bf(x-y) = cf(x) + dy , for all x,y real numbers.
Homework Equations
Well this is a functional equation, that I know. I have less experience with...
Oh my god, this is amazing. The physics is beautiful! It can be a pain if you don't understand it, or if you don't ask the right questions, or if you don't have a good physics teacher. Thank you all! You guys really helped me to understand. I am now 90% convinced that this is the way thing are...
Thank you! I have one more question. As I said, I am now aware that the flow of the current must be constant. But there is still something a little bit foggy in my head. I know that when passing through a battery a charge gains energy and I understood the concept of voltage. In my old picture...
That is a very good analogy, sir, thank you. So the presence of another person is very quickly noticed by the other person. He barely touches the floor with one toe and everybody is like: "go, go,go".
Good , you made this very clear and for that I'm deeply grateful. Another thing: when the...
I believe I understand now. My picture of electric flow is much clearer. But still, how comes that the intensity of the current is constant? While passing through resitors, why doesn't the current "slow down" ? How are we sure that the flow is indeed a constant ?
Don't get me wrong! I...
Well, I didn't solved it by factoring or polynomial division. I have solved as you did, by getting rid of the cubic term. But, my journey in learning how to do it and why it works, has gotten me through polynomial division. I stumbled in a quartic equation, but then I realized that I also don't...
@Ray Vickson and @NascentOxygen thank you very much for your explanations! It helped a lot, I managed to solve it and I have also learned how to divide polynomials, and why does it work:).
@Mark44 I really really respect and appreciate this forum, but I didn't have what to show. I tried to...
So, I'm trying to explain this to myself.
Ok, this is clear. So: I'm traveling up by elevator: I'm gaining gravitational potential energy. I'm climbing down the stairs: my potential energy is lost. But, let's suppose that by climbing down the stairs I don't get where I left from ; that is I...
So let's put it that way: let's say I travel to the top of the building. Say that I'm a lazy person , and for reaching the top I take the elevator. But when I go back, I take the stairs. When I first reached the top my potential energy raised. When I climbed down the stairs my potential energy...
Homework Statement
Solve the following equation:
x^4 + 12x^3 + 46x^2 + 60x + 20 = 0
Homework Equations
Well, I know how to solve simpler equations, in which the unknown dosen't appear at a power higher than 3. I tried to factor this polynom but I didin't suceed.
The Attempt...