0
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0answers
12 views

Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
1
vote
1answer
28 views

Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
1
vote
1answer
67 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
1
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4answers
43 views

Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
2
votes
1answer
61 views

What's the proper interpretation of canceling infinitesimals?

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
0
votes
1answer
12 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
0
votes
2answers
35 views

Physics Related Watt Question

A 550 kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts ...
0
votes
1answer
29 views

Deriving Barometric formula

Recall idea gas law: $pV= NkT$ where $p$ equals pressure, V volume, N moles of atoms, k boltzmann's constant, T temperature. Also, density: $\rho = m/V = \mu N/N_A V$ where $\mu$ is average mole mass ...
1
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1answer
47 views

Integrating this physics expression

Recall: $dp= \rho g \ dh$ where $dp$ is the change in pressure, $ \rho$ is the constant of density and $dh$ is the change in height. This is a part of fluid dynamics (buoyancy). I am to integrate ...
1
vote
2answers
34 views

Help verifying a the correct partial differentiation of $v_0=R\sqrt{\frac{g}{2h}}$

I have to use partial differentiation to solve the below equation: $v_0=R\sqrt{\frac{g}{2h}}$ Where $g$, $R$, and $h$, are defined as follows: $g=9.80 \frac{m}{s^2}$ $R=155 cm$ $h=116.2 cm$ ...
3
votes
1answer
62 views

Solving Wave Equation with Initial Values

I am trying to solve the wave equation: $u_{tt}$ = $u_{xx}$ With initial values: $u(x,0) =\begin{cases} x^3 - x, &\text{for }|x|\le 1,\ \\0, &\text{for }|x|\ge1\end{cases}$ $u_t(x,0) ...
0
votes
1answer
40 views

Finding the ideal angle for the maximum range of a projectile when elevated?

I was thinking about physics, and I thought of something. How do we find the ideal angle for the maximum range of a projectile when elevated? Assumptions: Parabolic flight path No air friction ...
0
votes
1answer
44 views

Using definite integrals with velocity and acceleration

Rocket A is traveling 49 ft/sec at 80 seconds. Rocket B is launched upward with an acceleration of $$a(t)=\frac3{\sqrt{t +1}}$$. At time t=0 seconds, the initial height of the rocket is 0 feet, and ...
1
vote
1answer
46 views

Does distance increase equally in equal time intervals under the influence of gravity?

Quick question. If an object falls under the influence of gravity near the Earths surface, is the distance traveled increased by equal amounts in equal time intervals? I thought that this would be ...
0
votes
3answers
37 views

Finding the total distanced covered (physics)

A subway train starts from rest at a station and accelerates at a rate of $1.60\frac{m}{s^2}$ for $14.0 s$ . It runs at constant speed for $70.0 s$ and slows down at a rate of $3.50\frac{m}{s^2}$ ...
1
vote
0answers
35 views

Define a plane with double integral

For my transport physics I have to describe how much volume through a rectangular pipe goes. The speed is given by $\displaystyle V_x=V_0 \frac{y}{h}$. But I have to define the plane with a double ...
0
votes
0answers
38 views

Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
0
votes
1answer
46 views

Problem with friction [closed]

Imagine two boxes stacked on top of each other. The bottom box is larger than the top box and it rests on a surface. So: Between the boxes is a friction force constant $\mu_s$ and between the ...
2
votes
1answer
34 views

Angle that car is at after angular acceleration

A car starts from rest on a curve with a radius of $150m$ and tangential acceleration of $\displaystyle 1.5\frac{m}{s^2}$. Through what angle will the car have traveled when the magnitude of its ...
1
vote
1answer
44 views

Vector functions applied to a football game

A wide receiver is standing $40$ ft to the left ($x=-40ft$) of the quarterback who is standing at the origin. The receiver immediately accelerates at $\displaystyle 9.79 \frac{ft}{s^2}$ at an unknown ...
0
votes
3answers
64 views

Finding velocity in optimization problem

Given $s=-16t^2+192t+144$, what is the velocity when $s=0$? This is part of a larger optimization problem which I solved, except for this last part. The critical point occurs at $t=6$, so after ...
2
votes
3answers
73 views

How do you solve this differential equation?

Though I've read questions on this site and really appreciate the quality of the answers, this is my first question, so I hope it follows the site's guidelines. When working with potential energy ...
0
votes
1answer
29 views

When to use trig substitution?

I'm trying to solve this physics equation: $$E=\frac {\lambda y} {4\pi \epsilon_{0}} \int_{-\frac l 2}^\frac l 2 \frac {dx} {({x^2+y^2})^\frac 3 2} $$ However, my calculus is a little rusty and am ...
2
votes
1answer
61 views

Physics and calculus?

A box slides down a slope described by: $$y = 0.05x^2$$ where $x$ is the x coordinate of the slope and y is the y co-ordinate (both in meters). Find the $y$ component of acceleration at $0.4 m$ if ...
3
votes
2answers
126 views

calculation of Stefan's constant

In the calculation of Stefan's constant one has the integral $$J=\int_0^\infty \frac{x^{3}}{\exp\left(x\right)-1} \, dx$$ which according to Wikipedia is equal to $\frac{\pi^4}{15}$. In this page of ...
0
votes
2answers
102 views

trouble understanding integration

I am reading through this physics book and have trouble understanding how they integrated one of the problems the conditions are Conditions: // ignoring the constant for simplicity $$r = \sqrt{x^2 + ...
-1
votes
2answers
51 views

Prove the average quantum mechanical energy using l'Hôpital's rule

I am trying to prove that taking the limit as $h\to0$ for the average quantum mechanical energy $$\dfrac{hν}{e^{hν/kBT}−1}$$ yields the average classical energy, $kBT$. How would you use l'Hôpital's ...
3
votes
1answer
111 views

Non-Linear ODE Strategy

I encountered the following $2^{nd}$-order, non-linear ODE while working on a classical mechanics problem: $$ \frac{d^2r}{dt^2}-\frac{\alpha^2}{r^3}+\beta=0 $$ where $\alpha \ \text{and}\ \beta$ are ...
0
votes
1answer
37 views

Vector functions and motion along a curve

A particle moves along the curve $x=\ln y$ with a constant speed of $4$ units per second. Find the normal scalar component of acceleration as a function of $x$. Honestly, what I don't understand ...
1
vote
1answer
207 views

Pumping Water out of Parabolic tank?

First of all, I understand how to do the integration part of this problem, but I am confused about the setup. Here is the question: Use integration to find the work done pumping all the water ...
0
votes
1answer
756 views

Calculus help. Find the work required to empty a cone shaped tank.

A tank in the shape of an inverted right circular cone (the ice cream goes on top) has height 7 meters and radius 3 meters. It is filled with 3 meters of hot chocolate. Find the work required to empty ...
2
votes
1answer
312 views

Solving differential equation regarding temperature change (Newton's law)

I'm solving a differential equation problem set and I bumped into the following DE problem where I got few question marks: The temperature of a body at time $t$ is $T(t)$ and the temperature of ...
0
votes
0answers
51 views

Solving physics problems using real and imaginary numbers

I was working on a particular physics problem and like we usually in physics do - replaced $\cos(x)$ with $e^{ix}$ and worked the result. When I tried to solve it without complex numbers I stuck. In ...
0
votes
1answer
54 views

Work done by gravitational force

In my calculus class we learned about line integrals, and for homework we have exercise to find work done by gravitational force on material dot with mass $m$ which follows path of the elipse ...
1
vote
1answer
114 views

Calculus Related Rates Question [duplicate]

A baseball diamond is a square with side length $90$ ft. A batter hits the ball and runs toward first base with a speed of $f(t)$ ft/s after $t$ seconds. At what rate is the batter's distance to ...
2
votes
1answer
43 views

Hankel trasformation of acoustic wave equation

We consider a simplified version of acoustic wave equation \begin{equation} \frac{\partial^2 p}{\partial r^2}+\frac{1}{r}\frac{\partial p}{\partial r}+\frac{\partial^2 p}{\partial z^2}+k^2 ...
1
vote
1answer
29 views

Deriving time and distance

The distance an aircraft travels along a runway before takeoff is given by $D=(10/9)t^2$, where $D$ is measured in meters form the starting point and $t$ is measured in seconds from the time the ...
2
votes
3answers
97 views

Velocity of a Particle

Consider a particle moving in a straight line from the fixed point $(0,2)$ to another $(\pi,0)$. The only force acting on the particle is gravity. How would we parametrically define the motion of ...
1
vote
0answers
73 views

Having trouble deriving 2d heat conduction problem

Basically, one of the problems stated to use the second law of thermodynamics to derive the laplace equation: $$\nabla^2_{r,\theta} = \frac{\delta^2}{\delta r^2} + \frac{1}{r}\frac{\delta}{\delta r} ...
1
vote
2answers
99 views

Why is acceleration $\frac{1}{2}at^2$ halved when finding final height (distance)?

The final distance of an object dropped from a certain height is: $$S_f=S_0-\frac{1}{2}at^2,$$ $S_f=$ Final distance $S_0=$ Initial height from which the object was dropped $a=$ acceleration due ...
0
votes
1answer
253 views

Fluid Forces using Calculus (Find Work Done)

A tank in the shape of an inverted right circular cone has height 12 meters and radius 11 meters. It is filled with 6 meters of hot chocolate. Find the work required to empty the tank by pumping the ...
3
votes
2answers
148 views

How to solve coupled linear ODE?

I wan to solve the following ODE's:- $$L_1 q''(t)+R_1q'(t)+\frac 1C_1 q(t)-Mq_2''(t)=V\sin(\omega t)$$ $$L_2 q_2''(t)+R_2q_2'(t)+\frac 1C_2 q_2(t)-Mq''(t)=V\sin(\omega t)$$ $L,C,R,V>0$, I already ...
0
votes
1answer
32 views

Obtaining $S(t)$ when $a(S)$ is given?

I have the acceleration as a function of distance, $a(t)$ $$a(t) = f(S)$$ $$\int v.dv = \int f(S).dS$$ And so I have velocity as a function of time if I want it. What I need is to find $S(t)$. I ...
4
votes
2answers
185 views

Work done propelling objects into orbit.

I am currently working on a few problems but as of now I am stuck and unsure what to do. My confusion isn't in the mathematical computations but in the question itself. My question that I am working ...
0
votes
2answers
111 views

Maths Homework Question Related to Physics

This is a physics question, but it's calculations. A 15kg child slides down a 2.3m -high playground slide. She starts from rest, and her speed at the bottom is 2.1m/s . What is the change in the ...
2
votes
4answers
36 views

Confusion with displacement of parabolas.

First I would just like to introduce my self and give you the extent of my mathematical background. I am currently a high school student that decided to self teach calculus. I am currently exploring ...
1
vote
3answers
91 views

Trouble with caculus problem, parametric equations, I don't know what I'm doing wrong

When a mortar shell is fired with an initial velocity of v0 ft/sec at an angle α above the horizontal, then its position after t seconds is given by the parametric equations $x = (v0 \cos \alpha)t$ , ...
3
votes
1answer
114 views

Force the moon exerts on the earth

Determine the force that the moon exerts on the earth. Note that since the diameter of the earth, 12,742 km, is not insignificant compared to the distance to the moon, 384,400 km, the gravitational ...
1
vote
1answer
759 views

Emptying water out of a Conical Tank? (Calculus)?

Please help me with this Calculus question. I'm not asking you to do the whole thing, but I just need help setting up the height function. Here is the question: A conical tank of radius $6$ feet and ...
0
votes
1answer
57 views

What is the rate of water pouring out of a drain after 28 minutes.

The floor drain is opened on a 24000-gallon pool. If the pool empties in 220 minutes then, according to Torricelli's Law, the volume of water $t$ minutes after opening the drain is given by ...