Initial Definition and 1000 Threads

Here is the question: Here is a link to the question: Calculus question on differential equations? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

Homework Statement http://postimage.org/image/466vu4yvp/ http://postimage.org/image/opdrmlv5n/ There can be more than one right answer Homework Equations α=Δv/ΔX v = v0 + αt The Attempt at a Solution Im having difficulty understanding the upward acceleration vector. Because I set the +y...

On a spacecraft two engines fire for a time of 572 s. One gives the craft an acceleration in the x direction of ax = 5.15 m/s2, while the other produces an acceleration in the y direction of ay = 7.41 m/s2. At the end of the firing period, the craft has velocity components of vx = 3782 m/s and...

Hi, I don't know what I'm doing wrong but these significant figures seem to be screwing me up. Problem: A bike rider accelerates constantly to a velocity of 7.5 m/s during 4.5 s. The bike's displacement is +19 m. What was the initial velocity of the bike? The textbook says the answer is 0.94...

Homework Statement A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm Determine the initial and final temperatures Homework Equations PVγ= nRT The Attempt at a Solution To get the initial...

Suppose we have the following IBVP: PDE: u_{t}=α^{2}u_{xx} 0<x<1 0<t<∞ BCs: u(0,t)=0, u_{x}(1,t)=1 0<t<∞ IC: u(x,0)=sin(πx) 0≤x≤1 It appears as though the BCs and the IC do not match. The derivative of temperature with respect to x at position x=1 is a constant 1...

Homework Statement 1.)I want to write a function in MATLAB that contains the 2nd order function: 20*d^{2}x;(dt^{2})+5*dx/dt + 20*x=0 (dampened spring) -The function should have 2 inputs (time,[initial values]) initial values should be a vector of 2 values -The function should...

Homework Statement Find a solution to the initial value problem that is continuous on the interval where Homework Equations I know the equations, but don't want to type them out.The Attempt at a Solution I got the first part of this question. The part where g(t) = sin(t) I can not figure...

Homework Statement See: http://www.aapt.org/physicsteam/2010/upload/2010_FmaSolutions.pdf #15, 16 Homework Equations U_o + K_o = U + K v_CoM = vM1 + vM2 / (M1 + M2) The Attempt at a Solution I thought that for 15 it was simply: 1/2mv^2 = mgh h = v^2/2g But this is wrong, so...

a ball is dropped twice off the same initial height. trial one bounces back with a velocity of 3m/s and trial 2 bounces back with a velocity of 2m/s. the time the ball is in contact with the ground for trial 1 is 0.01s. are the impulses on the ball the same for both trials or is it less in trial 2?

Homework Statement The unique solution to the initial value problem is http://webwork.usi.edu/webwork2_files/tmp/equations/ed/12ad7dca5df62ed3b18f5fbf8c6e871.png Determine the constant and the function Homework Equations Not sure for the second part. The Attempt at a...

Homework Statement A bullet of mass 12.0 grams is traveling with a speed V0 and strikes a block of mass M = 1.00 kg that rests on a horizontal surface (mu = 0.40). After the bullet imbeds in the block, it slides 2.60 meters before coming to rest. The initial velocity of the bullet must have...

Hello everyone, I'm new here so let me introduce myself first: I'm a games engineering student and my main field is programming Right now I'm struggeling with the N-Body Problem, well I think actually solved parts of it: I've implemented the basic equations with a leapfrog algorithm...

Homework Statement Solve the initial value problem: t(dy/dt)+8y=t^3 where t>0 and y(1)=0 Homework Equations None? The Attempt at a Solution It's a linear equation, so rearranged to dy/dt+8y/t=t^2. Took the integrating factor e^(∫8/tdt)=t^8 and multiplied through...

Homework Statement A child on a 4m long swing is pulled back 1m from the vertical and released with a push imparting a speed of 2m/s. Find an expression for the angle θ, as a function of time, identifying the frequency ω, amplitude θi, and phase constant δ. Homework Equations θ =...

Homework Statement A bean bag launcher is used to shoot a bean bag at a corn hole board. The bag is released at a height of .61m above the ground. The front of the board is 5.18m from the location where the launcher releases the bean bag. The back of the board stands .31 m off the ground; the...

Let X be an initial segment of a set A. By definition, if x is in X, a is in A and x>a then a is in X too. Can we say that some elements of A that are greater than x are also in X? Or X only consists of elements smaller than x?

Are those the same? if not, how do I calculate the initial yield stress from the tensile strength? all the materials properties I see on the web only specify tensile strength, and I need the initial yield stress as an input on non-linear FEA analysis. Is it possible to extract the initial yield...

Homework Statement Suppose that the initial vector P0 is not given and instead we are given that at time t=299 the state vector is P_299=[.1 .1 .8]. Than find P_300, the state vector at time t=300 Homework Equations I also know from the problem it is referencing that the transition...

Lets say we have a weight attached to a spring. When releasing it under water (whole motion occours under water) at different initial amplitudes, will logarithmic decrement be the same? And will the period change? I think it should be the same for different initial amplitudes. But...

In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? I...

Homework Statement A 0.0200 mol/L acid solution has a pH of 2.347. Calculate the percent ionization of this acid. Calculate the Ka of this acid The Attempt at a Solution I first calculated the hydronium ion concentration: 10^-pH = 10^-2.347 = 4.5*10^-3 I then used this concentration...

Homework Statement Solve for initial Value The attempt at a solution http://store2.up-00.com/Sep12/RjY55784.jpg

Homework Statement An object that is thrown covers a distance of 8.59 m. If the angle at which it is thrown is 23 degrees, what is its initial velocity? Homework Equations 5 kinematic equations: a = (v2-v1)/t d=0.5(v1+v2)t d=v1t+0.5at^2 d=v2t-0.5at^2 v2^2=v1^2+2ad Equation for...

Homework Statement A grasshopper jumps 1.00 meters from rest, with an initial velocity at a 45.0° angle with respect to the horizontal. Find (a) the initial speed of the grasshopper and (b) the maximum height reached.Homework Equations vx = v0xt = v0cos θ0 vy = v0 sin θ0 - gtThe Attempt at a...

Hi there, This is a problem concerning hyperbolic type partial differential equations. Currently I am studying the book of S. J. Farlow "Partial differential equations for scientists and engineers". The attached pages show my problems. Fig. 18.4 from case two (which starts in the lower part...

Homework Statement y''+4y'+6y y(0) = 2; y'(0) = 4 Homework Equations \alpha ± β = e^{x\alpha}(cosβx + sinβx) The Attempt at a Solution Auxilary equation is r^2+4r+6, which solves for -2 ± i I get the general solution: e^{-2x}(c1cosx + c2sinx) y' = -2e^{-2x}(c1cosx +...

Homework Statement A hydrogen atom in an excited state absorbs a photon of wavelength 434 nm. What were the initial and final states of the hydrogen atom? Homework Equations 1/λ=1/91.127 * (1/nf2-1/ni2) The Attempt at a Solution Tried to use the equation, but keeping the initial...

Homework Statement We are given a reaction: H2O2 + 2I- + 2H+ → 2H2O + I2 and are asked to find the initial number of moles of each reactant. V=10mL and C=0.2 mol/L for potassium iodide in the solution. V=5mL and C=0.5 mol/L for sulfuric acid in the solution. V=5mL and C=0.02 mol/L for...

Homework Statement An overdamped oscillator with natural frequency w and damping coefficient y starts out at a position xo>0. What is the maximum initial speed (directed toward the origin) it can have and not cross the origin? Homework Equations Overdamped Case Equation...

Homework Statement A known mass of methylamine, CH3NH2, was dissolved in water at 25 celsius 50.0 cm^3 of this solution was taken and titrated with 1.00x10^-1 mol dm^-3 hydrochloric acid solution, HCL(aq). The change in pH as an increasing volume of hydrochloric acid was added is shown in the...

Homework Statement Consider an electron that has its position measured to within a nuclear radius in a laboratory. What is the uncertainty in its position uncertainty one day later? Homework Equations The Attempt at a Solution What equation should I use to determine the...

Homework Statement This is a homework that has me completely stumped. If anyone help me out here, I would greatly appreicate it. A billard ball is east at 2.0 m/s. A second, idential ball is shot west at 1.0 m/s. The balls have a glancing collision (not head-on), deflecting the second ball...

Homework Statement I need help finding the x and y components of initial velocity being given the angle the trajectory was fired at and the distance the projectile traveled. For this example I'm using an angle of 15° and the projectile travels 0.534m. I'm not sure if I'm going in the right...

I have already solved the main portions. I have $$ T(x,t) = \sum_{n = 1}^{\infty}A_n\cos\lambda_n x\exp(-\lambda_n^2t) $$ The eigenvalues are determined by $$ \tan\lambda_n = \frac{1}{\lambda_n} $$ The initial condition is $T(x,0) =1$. For the particular case of $f(x) = 1$, numerically...

I've had to take diff eqtns now and I'm trying to get my head around Laplace again.. it's been a while. I can't seem to transition to the simplest step of partial fractions, my denominators are tough to figure out. If someone could point me to the next step that'd be great! Thanks a lot guys...

I am doing a projectile motion problem with my own results, and the unknown's of initial velocity and time. It is at 0 degrees, which I thought would mean I could find the vertical down of the projectile (where at an angle you find the vertical up and down because it goes up first). I have tried...

Homework Statement By trial and error, find a solution of the diffusion equation du/dt = d^2u / dx^2 with the initial condition u(x, 0) = x^2. Homework Equations The Attempt at a Solution Given the initial condition, I tried finding a solution at the steady state (du/dt=0)...

Homework Statement A cannon ball weighing 128 pounds is fired from a cannon at 45 degrees above the horizontal. The cannon ball lands in a pool that has a radius of 14 feet and located 7.5 feet above the ground. The closest edge of the net is 98 feet from the cannon. It takes 4 seconds for the...

1. Homework Statement A basketball player is standing 9.5 m from the basket, which is at a height of 3.1m. she throws the ball from a initial height of 2m at an angle of 35 degrees above the horizontal. The ball goes through the basket. Determine intial velocity. 2. Homework...

Homework Statement A basketball player is standing 9.5 m from the basket, which is at a height of 3.1m. she throws the ball from a initial height of 2m at an angle of 35 degrees above the horizontal. The ball goes through the basket. Determine intial velocity. PS Assume the max height of the...

Homework Statement A spring has a relaxed length of 0.17 m, and its stiffness is 15 N/m. The spring sits vertically on a table. You place a block of mass 0.058 kg on the spring and push down on the block until the spring is only 0.11 m long. You hold the block motionless on the compressed...

1. An arrow is shot vertically upward with an initial speed of 25 m/s. When it's exactly halfway to the top of its flight, a second arrow is launched vertically upward from the same spot. The second arrow reaches the first arrow just as the first arrow reaches its highest point. What is the...

Homework Statement In the figure below, what is the minimum initial speed of the dart if it is to hit the monkey before the monkey hits the ground, which is 12.2 m below the initial position of the monkey, if x is 48 m and h = 11 m? (Ignore any effects due to air resistance.) Use this figure...

Homework Statement Assume there is a wall located 100m downrange (x=100) from the projectile launching position (x=0) that is 55m (y=55) high. What is the minimum initial velocity of the projectile launched at what angle necessary to clear the wall? Homework Equations h=(v^2sin^2α)/2g...

*Messed up title, should have been find initial temp of copper* Homework Statement 8.00 g of aluminum at 200 °C and 18.0 g of copper are dropped into 50.0 cm3 of ethyl alcohol at 15 °C. The temperature quickly comes to 26.0 °C. What was the initial temperature of the copper? Density of ethyl...

Homework Statement A basketball player throws a ball at an angle of 30º above the horizontal. If the ball in has an initial velocity of 29.4 m/s, how far does it travel? Homework Equations Vyf^2 = Vyi^2 + 2(Ay)(Dy) solve for Dy and get [Vyf^2 - (Vyi^2)] / (2(Ay)) = Dy The Attempt at a...

In textbooks (such as Griffiths, for example), the general method for a solution to the Shrodinger's equation for a single particle, for some V(x), is given as : 1. Get the stationary state solutions 2. Combine them into a linear combination and figure out the coefficients from the known initial...

Homework Statement A projectile was fired across level ground at an initial angle of 43.00 degrees above the horizontal. During its flight, it reached a maximum height of 2974 metres. What was the initial speed of this projectile? Homework Equations I assume that the correct equation...

Homework Statement Consider the differential equation Find a general solution to this differential equation that has the form . . . y = Cx3 Find a second solution that might not be a general solution and which may have a different value of n than your first solution. The Attempt at a...