Hm, I still had problems finding the solution. I 'cheated' and used WolframAlpha to solve that last formula for theta.
Wolfram uses substitution and gives:
\theta = tan^{-1} \left ( \frac{ -V_i^2 \pm \sqrt{-g^2 x^2 + 2 g H V_i^2 + V_i^4}}{gx} \right )
WolframAlpha then states that...
Aha... yes, I didn't really want to solve for t, I just didn't see a way around it. Your approach is simple, and I'm dumbfounded I didn't realize it first ;)
However, it still seems to be an involved problem. Now we have:
t = \frac{x}{V_0}
Plugging this t into the formula for V_y, I...
Hi,
I've been muddling over this problem for a few days. I thought there would be a simple approach, but I'm having trouble reaching a solution. Here is the rundown:
We have a 2D projectile launcher. It hurls an object from the origin (0,0) at some initial velocity with magnitude V_i at angle...
Wow, was just testing around and it appears the exact same recursive formula satisfies the second part of the equation as well (the 'conjugate' square, I guess you could call it?). You just need to use the different set of initial values: n_i = 1, 5, 65, 901, 12545...
m_i = 0, 8, 112...
RamaWolf: Haha, nice! Yep, you identified where this problem stems from (I was sort of partitioning it up): http://projecteuler.net/index.php?section=problems&id=94
To find integer areas of the isosceles triangle \left( n, n, n-1 \right) one must solve (expanded from Heron's formula):Area =...
Hi,
I have a problem that I'm a bit stuck on, and need some direction:
I need to find \forall_n within a certain domain that can satisfy this equation:
\left( 3n-1 \right) \left( n+1 \right) = m^{2} where m,n \in \mathbb{Z}
Or, to put it in a different context, I'm looking for...
Homework Statement
Prove the \lim_{n\to +\infty}{\sqrt[n]{ n! }} \equiv \infty Homework Equations
uses well-known operations
The Attempt at a Solution
I think the best (easiest) approach is to find some f(n) \leq n! , and express it as some g(n)^{n} . This will then get rid of the...
Hi,
I need to solve the following integral from 0 to \infty :
Please note that my professor has defined log(x) = ln(x) , i.e. 10 is not the default base.
\int { e^{\frac{-log(x)^2}{2} } dx }
Through 'simplification' ( e^{log(x)} = x ), I have translated the function to:
\int { x^{...