Initial Definition and 1000 Threads

We have a metal sphere of radius R in the space and resistivity p. At a distance d>R from it we have antoher sphere of metal of radius r<<R and charge q. The 2 spheres intially are at rest. What is the initial potential energy between them? Now the sphere accelerate and collide anelastically...

Hi everyone, I'm trying to design a formula that determines the launch velocity, launch angle, and time spent in the air for a projectile if only the initial launch height, maximum height reached, and total horizontal distance traveled before the projectile hits the ground are known. It's not...

First of all this is probably the only time I will be on this forum. At first this seems a no brainer. But I am a weekend survivalist and I made a sling that can sling rock a little more then 1" in diameter 120 yards at an angle of about 50-55 degrees. After some research the type of rock I...

Hello everyone, I was doing some experiment using a spring compressed gun, that shoots up ball beraings. I made it using a desoldering pump and a PVC pipe,its quite small. ok, so I set it in 45° angles for maximum range. A desoldering pump has a spring inside, when you push down on top the...

When an electron and positron collides, they annihilate and produce photons, right? No massive particle can travel faster than light, So here is my confusion... Electrons and Positrons have mass and hence can never reach the Speed of light But When they collide they create photons. Which...

Homework Statement a human cannonball in 1940 soared over three ferris wheels, each 18 meters high covering a horizontal distance of 10.63 meters. Assuming that the point of projection is 2.50 meters above the ground and that he landed safely on a net placed at the same level, find his initial...

Hallo, I tried to use 'finite difference' method to solve a Initial Value Problem(IVP). For the two boundaries I used periodical condtion and for the differential operators I used 4th degree center approximations. But as result, I got this thing. Where comes this strange oscillation What do you...

I have been looking at an example of a initial value condition problem in my notes and don't really understand where the solution came from. Here is the question: Let z(x,y)= 2x+ g(xy) and add the initial value conditon, z= x on the line y=1. Find the general solution of the initial value...

Homework Statement A football player punts the football so that it will have a time of flight = 4.5s and land 45.7m away. The ball leaves the player's foot 1.52 m above ground. What is initial velocity? (Magnitude and direction) Homework Equations x-x_0 = v_0 * cosθ * t y-y_0 =...

I have a character who needs to jump to a certain height, I want to calculate his initial vertical velocity so that he can achieve that height. Distances and speeds are in logical pixels per second. The character's position is stored in a 2D vector \begin{pmatrix} x \\ y\end{pmatrix}, and...

Firstly, hello, I am new to the forum so please treat gently! I also not a physicist but am fascinated with quantum theory and particle physics. I have a few questions...(sorry if they have been asked before, but having read various threads I am still confused!) Here we go. 1. If a quantum...

Hello. I have gotten as far as to use the Laplace equation with these formulas, but I am having difficulty getting y and x to relate to each other. If requested, I can post my work, but I am sure it is fraught with mistakes. Help is very much appreciated! x' + 2y' - x - 2y = e^t x' - y' + x...

second ODE, initial conditions are zeros at infinity! I want to know the temperature profile of phase transition layer in the interstellar medium. For stationary solution, the dimensionless differential equation I ended up with is \frac{d^2T}{dx^2} = \frac{f(T)}{T^2} - \frac{1}{T} where f(T)...

In GR a object follows a geodesic when free falling as I understand. A object near the sun for instance wil fall to the sun following that line. If the initial speed is different the path will be different. How can it be that the geadesic is depending on the initial speed of the object...

Hey everyone, I'm a long-time visitor, it's my first time posting though. I have a homework problem that is causing me considerable consternation: (y^3)*(dy/dx)=(8y^4+14)*cos(x); y(0)=C Oh, and we're supposed to solve the initial-value problem, and then solve for the particular...

Radioactive sample activity is said decreases by factor 5 during 2-h interval. How to find the decay constant? If the given initial value is not given? I don't know how to calculate.

Could you advise a DSP book which explains state-space representation with initial conditions. Initial conditions part is important for me. Thanks.

Car A has twice the mass of Car B but only half as much Ek (Kinetic Energy). When both cars increase their speed by 6.00m/s their resulting Ek's are equal What were the initial speeds of both cars? ANS 1= 4.24m/s ANS 2= 2.12 m/sKe=1/2mV^2 m(a)=2m(b) Ek(a)=1/2Ek(b)...

1. My problem is I know displacement is 20m, acceleration is -5.4m/s, final velocity is 0m/s, coefficient of friction=0.55, the object slowing down weighs 1000kg, can I find initial velocity and the time it took to slow down and if so how? I have no idea how to go about this problem 2. Equations...

Homework Statement How to find the initial capacitor voltage if the capacitor is in series with a 1.5 ohm resistor, these 2 are in parallel with a reversed polarity 6v DC source, (reversed polarity - the negative terminal is pointing up) i assume the voltage across the resistor and capacitor...

Hi everyone, I am having trouble finding the answer to a homework problem. I don't seem to understand what the question is exactly asking for. The problem is: find the path of a particle with an initial position 10er + 1.0eϴ and an initial velocity 0.1er + 0.8eϴ

Acceleration -- all the energy is gravitational what speed was the ball thrown at? Homework Statement A ball is thrown up in the air and reaches a height of 2.2m assuming that all the energy is gravitational what speed was the ball thrown at. Homework Equations I cannot find the...

Homework Statement I need to calculate the initial velocity required to launch a projectile at a given angle from point A to point B. The only force acting on the projectile after launch will be gravity – zero air resistance. The projectile is launched within a simulated, virtual environment...

how to get to Vo = the square root of ((xa)/(sin2theta)) from the kinematic equations or form SinTheta =Voy/Vo CosTheta =Vox/Vo just really confused. I am writing a formal lab for my final and what I am asking is find the initial velocity it would take for the object to hit the target as a...

Homework Statement \frac{dy}{dx} = y^{\frac{2}{3}} with y(0) = y0 Homework Equations The Attempt at a Solution after separating variables: \frac{dy}{y^{\frac{2}{3}}} = dx then integrating: 3y^{\frac{1}{3}} = x + c and rearranging: y(x) = \left( \frac{x + c}{3} \right)^{3} after...

Homework Statement A train which weighs 1.4406E4N hit a car with a mass of1470kg. The cars skids 15m at angle of 68° to the crossing and the coefficient of friction between the tyres and the road is 0.25. Find the initial velocity of the car entering the crossing. Homework Equations...

A switch is closed in a voltage driven series LCR circuit. Will the initial current (j(0)) be 0, regardless of the type of voltage source? Will j'(0) = V(0)/L, where V(t) is the source voltage? Feedback much appreciated.

Homework Statement Homework Equations PE = mgh KE = \frac{1}{2}mv^{2} W = ΔKE W = Fd The Attempt at a Solution g = 9.80m/s^{2} hi = ? hf = 20.0m PEi + KEi = PEf + KEf mghi = mghf Would you then cancel the masses out? If you did, the initial height would be 20.0m...

Homework Statement For the space of continuous functions C[0,T] suppose we have the metric ρ(x,y) =sup _{t\in [0,T]}e^{-Lt}\left|x(t)-y(t)\right| for T>0, L≥0. Consider the IVP problem given by x'(t) = f(t,x(t)) for t >0, x(0) = x_{0} Where f: ℝ×ℝ→ℝ is continuous and globally Lipschitz...

Homework Statement Ernest Rutherford in his lab at McGill University, Montreal, fired alpha particles of mass 6.64 * 10^-27 kg at gold foil to investigate the nature of the atom. What initial energy must an alpha particle (charge +2e) have to come within 4.7 * 10^-15 m of a gold nucleus...

Homework Statement An object takes 12.3 meters to stop because of friction. Assume no skidding. If the coefficient of static friction is 0.86, what is the initial velocity of the object? Homework Equations initial velocity= mu*m*t The Attempt at a Solution

Homework Statement y'' +4y = 2 delta(t - pi/4) where y(0)=0 and y'(0)=0 Homework Equations Laplace transform Inverse Laplace transform The Attempt at a Solution after applying laplace tranform Y(s)=2e^((-pi/4)*s) / s^(2)+4 as the final answer i have y(t) =...

hey, i'm having trouble with this question, x y' - y = x2cosx the solution is y= xc + xsinx and we are asked to solve the equation in the following two cases, 1, y(0)=0 and 2, y(0) = 1 but applying these conditions to the general solution gives no information, in...

How can i get an initial speed without acceleration or time?? Homework Statement Hi..heres the problem: A 4WD traveling East has collided with a stationary car, the 4WD's skid marks are 15m long until the point of collision. The 4WD is sent 35degs South for 15.8m and the car is sent...

Homework Statement Hi..heres the problem: A 4WD traveling East has collided with a stationary car, the 4WD's skid marks are 15m long until the point of collision. The 4WD is sent 35degs South for 15.8m and the car is sent 55degs North for 15m. The car has a mass of 1150kg and the 4WD's is...

Homework Statement A golfer hits a ball, giving it a maximum height of 20 m. If the ball lands 130 m away at the level from which he hit it, what was its initial velocity? (Neglect air resistance) Homework Equations The Attempt at a Solution I found the angle to be 31.6, so I...

Homework Statement Solve the matrix of differential equations with given initial values. dx/dt= (-6 2) x (-3 -1) Initial value is x(0) = -2 -5 Homework Equations (A-λI)=o The Attempt at a Solution My eigenvalues are -4 and 3 My...

1. Homework Statement A soccer ball is kicked at 38.0° with respect to the horizontal and travels 64.0m before striking the ground. a) what is its initial velocity? b) how long was it in the air? 2. Homework Equations dv=1/2*at2 dh=Vh*Δt Kinetic equation d=Vi*t+ 1/2*at2...

Homework Statement A soccer ball is kicked at 38.0° with respect to the horizontal and travels 64.0m before striking the ground. a) what is its initial velocity? b) how long was it in the air? Homework Equations dv=1/2*at2 dh=Vh*Δt Kinetic equation d=Vi*t+ 1/2*at2 dh=-V2*sin2θ /g...

so i have been studying chaotic system in class, and i just want to know if we change the initial conditions of a chaotic system can it become non-chaotic? I think yes because, chaotic system is sensitive to initial condition hence it would have an effect on the chaotic behavior. I'm I...

Homework Statement y''-4y'+4y=0 , y(1)=1 and y'(1)=1 The Attempt at a Solution Auxiliary equation: r2-4r+4=0 I tried factoring 2 different ways: (r-2)2=0 r=2,r=2 y1=e2t y2=y1 y(t)=c1e2t+c2e2t y(1)=c1e2+c2e2=1 ---eq(1)y'(t)=2c1e2t+2c2e2t ...c2=1/(2e2)-c1 ---eq(2) sub eq(2) into eq(1)...

Homework Statement In a particular star forming cloud the initial mass function (IMF) is given by N(M_{*})=Cexp(-M_*^2) where C is a normalisation constant. (The IMF describes the initial relative number of stars of different masses). Assuming that the number of hydrogen Lyman continuum...

Homework Statement Solve: dy/dy = y^3 given the initial condition y(0)=0 The Attempt at a Solution \int \frac{dy}{y^3} = \int dt \frac{-1}{2y^2} = t + c y^2 = \frac{-1}{2(t+c)} y = ± \sqrt{ \frac{1}{2(-t-c)}} This equation isn't going to support the initial condition, so can someone tell me...

Hi, I've got a problem here, that I'd like to discuss before trying to implement any sort of solution. Basically I've got a planetarium simulation, in which I'd like to plot a patched conic trajectory ahead of a spacecraft . The planetarium only simulates two-body gravity, and switches...

Given: Solve the initial value problem 2(√x)y'+y+4(√x) ; y(1)=2 I am having trouble separating the x's and y's in order to integrate. I keep coming up with: dy/dx +y/(2(√x))=2... What do I keep missing here? I am pretty sure you leave the y(1)=2 alone until you are finished with...

Homework Statement Solve the following differential equation with the given initial value y(0)=0Homework Equations 2sinxy dx + (x2 cos y - 1) dxThe Attempt at a Solution I am getting stuck trying to find the integrating factor

Homework Statement Solve the following Initial Value problem for x(t) and give the value of x(1) Homework Equations (dx/dt)-xt=-t , x(0)=2 The Attempt at a Solution (dx/dt)-xt = -t (dx/dt) = xt-t (dx/dt) = t(x-1) (1/(x-1)) (dx/dt) = t (1/(x-1)) dx = t dt Then I integrate...

Homework Statement Find the initial speed (Vo) in Projectile motion in terms of Gravity (g) Height (H) Range (R) Homework Equations Nothing has been given, however, have found these so far... Initial Velocity = sqrt((1/2 * g * R^2)/(cos2θ * (R * tanθ + H)) And a few others which are...

Homework Statement .019 Kg icecube @ unknown temperature (In deg C) Placed in 200 mL (.2 KG) water at 35 C. After melting, water is at 22.4 C. Find initial temperature of ice using conservation of energy. Homework Equations I've done the math a ton of times and keep getting -60 C...

how can we solve this ODE? http://img818.imageshack.us/img818/3966/59962234.png