# Tagged Questions

Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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### Projectile Motion Question [closed]

A ball is thrown towards a vertical wall which is a horizontal distance $d$ from the point of projection. The initial speed is $u > 0$ and the angle of projection is $0 < \alpha < \pi/2$. The ...
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### Moving oil out of a conical shaped tank

I need some help finishing out a Calculus problem. I'm not sure how $d$ works (single value, or integral) at the end. A conical shaped tank, with its apex pointing upward is one fourth full of ...
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### Probability distribution obtained by repeatedly sampling $S_x,S_y$ on a spin-$S$ system

While trying to rework an upcoming quiz problem for a quantum physics course, I came up with the following question which turned out to be harder than I expected. (Note: I take $\hbar =1$ in all ...
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### Airplane decelerating as a function of speed

So, I have a problem where an airplane is decelerating as a function of speed. The acceleration is described as $a=dv/dt=-0.0035v^2-3$ as a function of time. For $t=0, v=83.3$ m/s. Can someone help me ...
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### Is the following derivation of how to find $v$ given $a=v'$ wrong?

My physics professor did the following: Let $a(t)=v'(t)$ be a given function. Suppose $v(0)$ is known, then $$\int_{v(0)}^{v(t)} dv=\int_0^ta(t)dt \iff v(t)=v(0)+\int_0^ta(t)dt$$ I believe ...
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### How to solve ODE

Solve the DE: $$2y^2y''+2y(y')^2=1$$ Is it possible to solve this by implicit substitution i.e. let $v = y'$ and thus $$\frac{dv}{dy}v = \frac{1-2yv^2}{2y^2}$$ by the chain rule. And then from ...
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### Calculation of the velocity of an object

I have the position function $$s(t) = -4.9t^2 + v_0t + s_0$$ for free falling objects. The question is what is the velocity of an object after $5$ seconds with initial velocity $120$ m/s. I tried to ...
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### elastic strings and springs mechanics problem.

This is an example given in Edexcel M3. In question below length =1m and λ=10N but the given answer(Circled in red) it looks like the value of λ multiplied by 2. I couldn't figure it out why? Need ...
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### Schrödinger's equation denumerable eigenvalues

The Schrödinger's equation can be written in this form: $-u''(x)+V(x) u(x) = E u(x)$ $V(x)$ is a function that is defined on the real line. We know ${u}^{2}$ is integrable on the whole real line. ...
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### normalisation constant of SE for infinite square well

we fix arbitrary constant A by normalizing wave function $\displaystyle \int_{0}^{a}|A|^2sin^2(kx)dx = 1$ by using identity $sin^2(x) = \displaystyle \frac{1}{2}-\frac{1}{2} cos{2x}$ we can ...
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### Problem with 4-body Matlab code

I'm trying to model the 4 body problem to see how Jupiter, Earth and Mercury orbit the Sun. I found a two body script and adapted it as accordingly to modify my problem, but for some reason the ...
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### Identity in continuum mechanics

For a problem in the textbook I am reading, I need to prove that $\int_Vw_{i,j}v_jdV = \int_Sw_iv_jn_jdS$, where $S$ is the boundary of the volume $V$, $v_i$ is the velocity vector field of a ...
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### Falling objects - finding the speed [closed]

I am trying to work out how fast water will be falling by the time the water hits the ground. If it starts 100m high how fast would it be travelling and why? With the acceleration because of gravity ...
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### Result from derivatives seem inconsistent

I'm working on a physics problem that looks like this For some context we have a person on his sled represented in our first term. The second term represents the velocity of a stone thrown backwards ...
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### Questions on energy conservation of the wave equation

I'm reading this book. In Ch. 3.4, it studies the wave equation $u_{tt}=c^2u_{xx}$ with BCs $u_x(0,t)=0,\,u_x(L,t)=0$, and ICs $u(x,0)=f(x),\,u_t(x,0)=g(x)$. The total energy of a string is the ...
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### Why is “$\pi^2= g$” where $g$ is the gravitational constant?

Some months ago a professor of mine showed us a 'proof' of why $g\approx 9.8 ~\text{m}/\text{s}^2$ (the gravitational acceleration at the surface of the Earth) is 'equal' to $\pi^2\approx9.86\dots$ ...
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### Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
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### virtual work and potential energy

I was just going through the thermal and elastic buckling of bars & plates ,I found some researchers use virtual work to derive the equations, another researchers use potential energy in other ...
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### Mechanics - Motion round a vertical circle [closed]

A ball of mass 100 grams is hanging from a fixed point by a string 2.5 metres long. It is struck with a bat so that it starts to describe a circle in a vertical plane. When the ball reaches a height ...
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### Physics Velocity Correction

So, been up all night working on getting the velocity/angle of arrow simulations perfect. Running into an issue with the physics engine I'm using is ever so slightly off (probably a rounding issue) ...
The velocity $\displaystyle\vec{v}$ of a particle $=\frac{d\vec{x}}{dt}$. So surely this means that $\vec{v}$ is dependent on the position of the particle?