Initial Definition and 1000 Threads

Homework Statement x(dy/dx) = 3y +x4cos(x), y(2pi)=0 Homework Equations N/A The Attempt at a Solution I've tried a couple different ways to make this separable, but you always carry over a 1/dx or 1/dy term and I can never fully separate this. I've also tried to do a Bernoulli differential...

Homework Statement How do Initial and Final Kinetic Energy depend on each other? Homework EquationsThe Attempt at a Solution Do they remain equal? For example for the same mass m, can we write KE1 = KE2 1/2 m v1^2 = 1/2 m v2^2

Homework Statement Find the initial velocity of the boost phase (when water is coming out). Here is everything I know - Mass of rocket with no water is 0.13kg, mass of rocket with water is 1.1kg. The total length of the rocket is 0.48m. The time to the maximum point is 3.46 seconds, and total...

$\begin{align*}\displaystyle y'&=y-5\quad y(0)=y_0\tag{given}\\ y'-y&=-5\\ u(x)&=\exp\int-1\, dx = e^{-t}\\ (e^{-t}y)&=-5e^{-t}\\ e^{-t}y&=-5\int e^{-t} dt = -5e^{-t}+c\\ &y=-5\frac{e^{-t}}{e^{-t}}+\frac{c}{e^{-t}}\\ y&=\color{red}{5+(y_0-5)e^t}...

$1.1.2c\\ \displaystyle \frac{dy}{dt}=2y-10, \qquad y(0)=y_0$ rewrite $\quad\displaystyle y'-2y=-10$ obtain u(x) $\quad\displaystyle u(t)=\exp\int -2 \, dt=e^{-2t}$ integrate using the boundaries: $\quad\displaystyle \int_{y_0}^{e^{-2t}y}\,du=-10\int_{0}^{t}e^{-2v}\,dv$...

$\displaystyle \frac{dy}{dt}=2y-5, \quad y(0)=y_0$ rewrite $$y'-2y=-5$$ obtain u(x) $$u(x)=\exp\int-2\, dx = e^{-2t}$$ then $$(e^{-2t}y')=5e^{-2t}$$ just reviewing but kinda ?

If all matter was at maximum density, would not the temperature have been extremely cold of the sum of all matter? temperature affects density I think.

2000 (a) Find the solution of the given initial value problem in explicit form. $$xdx+ye^{-x}dy=0, \quad y(0)=1$$ \begin{align*}\displaystyle xdx&=-ye^{-x}dy \\ \frac{x}{e^{-x}}\, dx&=-y\, dy\\ xe^x\, dx&=-y\, dy \end{align*} (b) Plot the graph of the solution $\quad...

Homework Statement Homework Equations The Attempt at a Solution I solve question a) by rearranging the F=m*a equation, which makes the acceleration equal to (24N/18kg)=1.30m/s^2. And I find the final speed using equation W=1/2*m*v^2 and rearranging it to solve for v, which gives me a value...

Hello All, Firstly, what a wonderful place for people to help one and other. I am glad that I have stumbled across : ) I have posted this query in advanced because to me there it is advanced but if it is basic to others then please excuse me. I can easily work out the probability of...

Homework Statement Then we are asked to determine the initial discplament, velocity and acceleration of the midpoint of the string. Homework Equations I guess we should use equation x(t)=Asin(wt+phi) The Attempt at a Solution My attempted solution is to use the above equationa and put t=0...

Hi, I am reading Landau-Lifshitz course in theoretical physics 1. volume, mechanics. The mechanics is derived using variatonal principle from the start. At first they start with point particles, that do not interact with each other. Thus the equations of motions must be independent for the...

Homework Statement A drunken driver crashes his car into a parked car that has its brakes set. The two cars move off together (perfectly inelastic collision) for 6.0 m. If the mass of the moving car is 1030 kg and the mass of the parked car is 1410 kg how fast was the first car traveling when...

1. Homework Statement The Initial Mass Function (IMF) defines the distribution of stellar masses created in a star-forming event. The probability P(m)dm of forming a star with a mass between m and m + dm is given by P(m)dm = km−α dm where α is the exponent of the power law and k is a constant...

Homework Statement An archer launches an arrow from coordinates ##(0, 0)## at an angle ##\alpha## and with an initial velocity ##v_0##. There's a target located ahead of the archer and the center of that target is at coordinates ##(d, h)##. At what ##v_0## and at what angle ##\alpha## does...

Homework Statement [/B] After a completely inelastic collision between two objects of equal mass, each having an initial speed of v, the two move off together with a speed of v/3. What is the angle between their initial directions.Homework Equations Conservation of momentum in both x and y...

Homework Statement Let ##b_1\in \mathbb{R}## be given and ##n=1,2,\dots## let $$b_{n+1} := \frac{1+b_n^2}{2}.$$ Define the set $$B := \{b_1\in\mathbb{R} \mid \lim_{n\to\infty}b_n \text{ converges}\}$$ Identify the set ##B##. Homework EquationsThe Attempt at a Solution I claim that ##B =...

Hi all! I need to give a presentation on a problem in class and @countryboy helped me to figure out most of it, I only have one remaining question. Here it goes: Consider the system dr/dt = -j, dj/dt = r , where r (t) represents Romeo’s love (positive values) or hate (negative values) for...

Homework Statement Determine the initial velocity of a projectile that reuturns to launch level 10.0 seconds after it is launched and lands 300.0m away from the launch site. Homework Equations Δx=v0xt Δy=v0yt+1/2gt2 The Attempt at a Solution [/B] 300=v0x(10) v0x=30m/s I don't...

Homework Statement Find the initial velocity v0x such that the particle will have the same x-coordinate at time t= 4.07 s as it had at t=0. The acceleration of a particle is given by ax(t)=−2.00 m/s2 +( 3.09 m/s3 )t. Homework Equations v = v0 + a t Δx = ((v+v0)/2)t Δx = v0t + 1/2at^2 v^2 =...

1. Vo Mass=m 2.So we tried two ways of doing this, one is by taking the y component of the i itial velocity and using that and the other by using the component of its weight parallel to the initial velocity.They give conflicting answers. For the left one it turns out to be t=Vosinθ/g But for...

Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model. I have attached my attempt to this post. It is quite long and...

Homework Statement The moving proton hits the second proton, which we consider to be stationary. In the moment of central strike gap between the protons is 10(-13)m. What was the initial speed of the moving proton? Proton mass is 1.67*10(-27)kg and charge 1.6*10(-19) C. Homework Equations...

$\tiny{de1.2.1}$ $\textsf{ Solve each of the following initial value problems and plot the solutions for several values of $y_0$.}\\$ $\textsf{ Then describe in a few words how the solutions resemble, and differ from, each other.}\\$ $$\begin{align*}\displaystyle \frac{dy}{dt}&=-y+5...

Hello! (Wave) I want to prove that if for the initial value problem of the wave equation $$u_{tt}=u_{xx}+f(x,t), x \in \mathbb{R}, 0<t<\infty$$ the data (i.e. the initial data and the non-homogeneous $f$) have compact support, then, at each time, the solution has compact support. I have...

Hello! (Wave) I want to find the solution of the following initial and boundary value problem: $$u_t(x,t)-u_{xx}(x,t)=0, x>0, t>0 \\ u_x(0,t)=0, t>0, \\ u(x,0)=x^2, x>0.$$I have done the following so far: $$u(x,t)=X(x) T(t)$$ $$u_t(x,t)=u_{xx}(x,t) \Rightarrow...

$\tiny{2.1.{7}}$ $$\displaystyle y^\prime +y =\frac{1}{1+x^2}, \quad y(0)=0$$ $\textit{Find the solution of the given initial value problem.}$ \begin{align*}\displaystyle u(x) &=e^x\\ (e^x y)'&=\frac{e^x}{1+x^2} \\ e^x y&=\int \frac{e^x}{1+x^2}\, dx\\ %\textit{book answer} &=\color{red}...

Hello! (Wave) I want to solve the equation $u_t+u^2u_x=0$ with $u(x,0)=2+x$. I have tried the following: The characteristic curves for $u_t+u^2 u_x=0$ are the solutions of the ode $\frac{dx}{dt}=u^2$. We have that $\frac{d}{dt}u(x(t),t)=0$, implying that $u(x(t),t)=c$. The characteristic...

Homework Statement In the circuit shown,the initial charge on the capacitor is Q0 = 200μC . If the switch is closed at t=0 , the capacitor starts discharging through the resistance R=4MΩ . What is the initial current (in μA) (i.e. at t=0) in the circuit? Homework Equations I = I0 e-t/τ τ =...

Hello! (Wave) We consider the initial value problem $$x'(t)=-y(t), t \in [0,1] \\ y'(t)=x(t), t \in [0,1] \\ x(0)=1, y(0)=0$$ I want to solve approximately the above problem using the forward Euler method in uniform partition of 100 and 200 points. I have written the following code in...

Homework Statement Homework Equations ##J=\frac{I}{A}## A=π r2 The Attempt at a Solution Since I is constant and the diameter is doubled , A2 = π (##\frac{2D}{2}##)2 A2 = 4 A1 J2 = I/(4A1) = J1 /4 → (E) Is my answer correct ?

Homework Statement Homework Equations W =ΔKE The Attempt at a Solution found work done by spring -1.3 =ΔKE -1.3 = KEFINAL - KEINITIAL -1.3 = .5(0.25)(VFINAL2) - .5(0.25)(VINITIAL2) Since v final is 0 since it stops momenteraly at the bottom of the spring -1.3 = - .5(0.25)(VINITIAL2)...

Information Given:Zero, a hypothetical planet, has a mass of 4.2 x 1023 kg, a radius of 2.8 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. Question: (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its...

Hi all, I've been tasked with computing binary star orbits based on their initial parameters, positions and velocities. In this problem everything must be expressed in terms of the masses, but I am struggling to define positions and velocities in terms of mass. It is assumed that the stars are...

Homework Statement Suppose an object has a charge of 1 C and gains #9.38 ✕ 10^18# electrons. When another object is brought in contact with the first object (after it gains the electrons), the resulting charge on the the second object is 0.9 C. What was the initial charge (in Coulombs)...

Say I dissolve NaOH in water - a very exothermic reaction. Does it matter if I dissolve it in water that is at room temperature or at a different temperature? Will changing the initial temperature of the water affect the dH of the reaction (hence affect the change in temperature at the end of...

<Moderator's note: Moved from a technical forum and thus no template.> I'm not sure how they got the extra (1/2)mv^2? My question is shown using pink font in the image below as well as my attempt.

Homework Statement A capacitor with initial charge q0 is discharged through a resistor. What multiple of the time constant τ gives the time the capacitor takes to lose (a) the first 1/8-th of its charge (b) 7/8-th of its charge? Homework EquationsThe Attempt at a Solution since ı know...

Homework Statement Hello, so I’ve been trying to find some possible way to calculate this: The initial Velocity and angle needed to launch a projectile and reach the coordinates (x,y). The maximum height the ball can reach before it starts to head down to the target value should be y+5m The...

Hello, I'm a beginner on SGR and I'm struggeling with this, probably, simple problem. I'm interested on exploring Field Theory ( relativistic) so I started reading http://www.elegio.it/mc2/LandauLifshitz_TheClassicalTheoryOfFields_text.pdf which was suggested and reccomended by a PF's member...

Homework Statement [/B] Assume that we have 137 Cs absorbed in an unknown organ. We know that the initial dose rate is 1μGy/h. Calculate the total equivalent dose in this organ, if we know that the activity is reduced exponentially over time with an active half life of 100 days. Homework...

Homework Statement So! The problem states that a grasshopper jumps from the edge of a table. We know that x-initial is zero and x-final is 1.06m. This is how far he jumped from the origin. The height of the table is unknown, but we know that the height of the grasshoppers jump with respect...

Homework Statement Homework Equations ## y(t)\mu(t) - y(t_0) \mu(t_0) = \int_{t_0}^t \mu(s) g(s) ds## ## y(t) = \frac{1}{\mu(t)} \left[y_0 \mu(t_0) + \int_{t_0}^t \mu(s)g(s) ds\right]## The Attempt at a Solution (7 lines)I have done the first part, which seems correct, yet I am stuck with...

Homework Statement Homework Equations W=mg F=ma The Attempt at a Solution I'm not sure how I should be answering this problem, and the diagram itself looks odd. I was thinking about how it would work in real life, since the biggest pulley is attached to the leftmost pulley, by the same...

Homework Statement Homework Equations [/B] T = inertia * alpha The Attempt at a Solution I'm not sure how the torque or angular velocity initially affects the time to speed, but it seems like the more angular velocity , then the quicker the engine would stop. I do know that more torque...

Homework Statement A projectile is launched: Horizontally, with an average displacement of 49 cm Vertically, with an average displacement of 28 cm At a 23 degree angle, with average displacement of 126 cm Homework Equations The Attempt at a Solution I am sad to say I don't know how to do it...

Homework Statement In 1940, Emanuel Zachinni, one of a family of “human cannonball” performers, set a world record by traveling 53m. If he clears the 20 m tall ferris wheel (which is 25 m away from the cannon) by 10 m, how fast was he going at launch? Homework Equations range 53m...

Hello Guys, We haven't yet covered on how to solve 2nd order equation in class however we have this assignment given to us. Any tips would be appreciated for these 2 little problems. 1. Homework Statement We have this initial Equation: d2y/dt2−7dy/dt+ky=0, and we need to find the values of k...

Homework Statement A boy release ball A from height 5m from ground at the same time other boy throw ball B vertically upward to exactly strike ball A. When ball B released it was 1m from ground find minimum initial velocity of ball b. Given g=10m/s^2 a) 2m/s b) 3m/s c) 4m/s d) 5m/s Homework...

Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ? Thanks!