Initial Definition and 1000 Threads

A ball thrown vertically from ground level is caught 3.0 s later by a person on a balcony who is 14 m above the ground, determine the initial speed of the ball. When I first tried doing this problem, I tried using the speed equation of distance/change in time, so I divided 14 by 3 which gave...

Homework Statement Solve the initial value problem: x^{2}{y}'' + x{y}' + y = 0, x>0, y(1)=1, {y}'=2 Homework Equations y=x^m The Attempt at a Solution x^{2}(m(m-1)x^{m-2})+xmx^{m-1} + x^{m} x^{2}(m(m-1)x^{m-2})+xmx^{m-1} + x^{m} x^{m}(m(m-1) + m + 1)...

Dear All, I would like to do an exponential function least-squares fitting, but having two or more exponents. For example the function looks like this: y (x) = A \exp (-x/a) + B \exp (-x/b) where A, a, B and b are the least-squares fitted parameters. My question is how to obtain the...

Homework Statement A dog jumps a distance, L, and a maximum height, H, where the dog only has horizontal velocity when it travels through the hoop. What is the speed of your dog when he leaves the ground? What is the speed of your dog when he goes through the loop? Both answers should NOT...

Homework Statement The unique solution of the linear system of differential equations ##\frac{dv}{dt}=-34v+ -16w, v(0)=-1## ##\frac{dw}{dt}=80v+ 38w, w(0)=-3## is: (enter the smaller of the eigenvalues first, and note that all entries here are integers) ##v(t)= C_1 e^{-2t}+C_2 e^{6t}##...

Homework Statement Find f(t) for the function F(s)=(10s^2+85s+95)/(s^2+6s+5) and apply the initial and final value theorems to each transform pair Homework Equations Initial value theorem: f(0)=lim s->∞ s(F(s)) Final value theorem: f(∞) = lim s->0 s(F(s)) The Attempt at a Solution...

(If the equation below do not appear correctly, you can read all of the question in the attached file.) Solving the time dependent 1D Schrödinger equation, one can show that in all points (x,t), i\bar{h}\frac{\partial}{\partial t}\Psi(x,t)=-\frac{\bar{h}^2}{2m}\frac{\partial^2}{\partial...

Homework Statement I want to cover a distance of 8,ooo,ooo,ooo,ooo m and I want to know the time it will take if I have an initial velocity of 176400 m/ sec with an acceleration of 19.6 m/sec2. I think I have the right equation here I'm just not sure how to solve for t. Could someone walk me...

Homework Statement http://imgur.com/Mwin7dB http://imgur.com/Mwin7dB Homework Equations The Attempt at a Solution This is a fairly simple problem. My issue is that I can't identify the second initial condition. The first one is simple. At t=0, the voltage on the capacitor is...

Mod note: Reinstated problem after poster deleted it. [/color] Homework Statement Just wondering if I did this correctly: ##y''+4y'+4y=e^{x}## and initial conditions ##y(0)=0; y'(0)=1## Homework Equations The Attempt at a Solution So I found the characteristic equation to be...

Please see attached for question. My problem is the initial displacement. i am told the first step is this kx + c(dx/dt) = unit impulse laplace transform kX + c(sX-x0)=1 from that i can see the initial displacement is included in the damper but why isn't it included in the...

Homework Statement Solve the following DE y'' + 8y' − 9y = 0, y(1) = 1, y'(1) = 0 Homework Equations Homogenous DE with constant coefficients The Attempt at a Solution Well, i solved it normally using a CE and having yH= c1 e^t + c2 e^(-9t) .. y' = c1 e^t -9 c2 e^(-9t)...

Homework Statement A 7.00 g bullet, when fired from a gun into a 1.10 kg block of wood held in a vise, penetrates the block to a depth of 6.40 cm. This block of wood is next placed on a frictionless horizontal surface, and a second 7.00 g bullet is fired from the gun into the block. To what...

$ kxy \frac{dy}{dx} = y^2 - x^2 \quad , \quad y(1) = 0 $ My professor suggests substituting P in for y^2, such that: $ P = y^2 dP = 2y dy $ I am proceeding with an integrating factor method, but unable to use it to separate the variables, may be coming up with the wrong integrating factor ( x )

A ball is thrown at an unknown speed at an angle of 30 degrees. The initial and final height from the ground is 0 meters. What speed should the ball be launched at in order for it to land on the ground 3 meters from the launch point? Here is what I tried...

Homework Statement I need to find the initial acceleration of a steel object that weighs .89 kg, that is pulled along a steel a rail by a cord. The cord is at an 45 degree angle and has a tension of 21 N. The friction coefficents(spelled right?) of steel on steel are: .8 for static friction...

I've got a few small questions I'd like to straighten out. I'm really trying to establish a firm procedure involving the steps I write down because I find it helps me learn the math and avoid errors. Solve the initial value problem: (x+y)^2 dx +(2xy+x^2-1)dy = 0 with y(1)=1 So let M(x, y)...

Homework Statement They give me y ' = (xysinx)/ (y+1) , y(0) = 1 Homework Equations So I just separated and integrated The Attempt at a Solution I'm 99 percent sure I'm OK up till here. I just wanted to get an explanation for something. I was wondering my answer is y + ln(y)...

Homework Statement (A) The damped oscillator is described by the equation mx''+bx'+kx=0. What is the condition for critical damping expressed in terms of m,b,k. Assume this is satisfied. (B) For t<0 the mass is at rest (x=0). This mass is set in motion at t=0 by a sharp impulsive force so...

L \frac{di}{dt}+Ri=E and we're given i(0)=i_o I,R,E,i_o are constants. So I rewrite equation as \frac{di}{dt}+\frac{R}{L}i=\frac{E}{L} therefore P(i)=\frac{R}{L} let \mu(x)=e^{\int \frac{R}{L}dt}=e^{\frac{tr}{L}+C} multiply equation by integrating factor to get e^{\frac{tR}{L}}...

Homework Statement A baseball is thrown just so that it is able to pass a wall 10m high at a distance that is 1000m away. If it is aimed 30 degrees above the horizontal, what is the initial speed of the baseball? Homework Equations relevant equations shown at the attempt at the solution...

Hi, I'm designing a propulsion system for an electric car as a part of a college project. I'm trying to find the minimum torque needed so the car can begin to move, I'm assuming this will be the greatest torque required for motor selection, provided the vehicle will accelerate relatively...

Homework Statement Given: A sealed, rigid container (cannot change shape or size) containing steam at the shown conditions has heat added until it reaches the final shown state. Determine: a) heat added, b) work performed, c) change in internal energy of the system, and d) final system...

Homework Statement Solve \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) for x>0 and t>0 if w(x,0) = f(x) w(0,t) = h(t) Homework Equations The Attempt at a Solution I know how to solve for the conditions separately and that would give...

Ok, I have a practice exam... My professor gave out a copy with worked out examples. There is one where I don't get his logic at all. I was wondering if you guys could explain it to me?\(\displaystyle (\frac{1}{t}+2y^2t)dt+(2yt^2-\cos(y))dy=0\) First, he put \(\text{Assume t>0}\) ...

Homework Statement An ball is launched at a 45 degree angle with an initial speed v0. What is its speed at its max height? Homework Equations n/a The Attempt at a Solution This problem does not contain any calculations. I was wondering if somebody could explain how the speed at...

I'm having trouble with this problem... I am almost certain that I have the first part correct which is solving the first order DiffEQ using an integrating factor. I think that I am computing the constant incorrectly. I have followed all steps, including the similar problem given on WileyPlus...

Homework Statement You now place the launcher on the floor and shoot a steel ball at an angle of 45°. If you had previously measured an initial velocity of 3.3 m/s for this launcher, then how far from the launcher do you expect the ball to hit the floor? Homework Equations I can't find...

Homework Statement http://www.whoisntdavidrinaldi.com/Untitled.png Homework Equations The Attempt at a Solution So I had to use this initial momentum and multiply it by a plane wave (sure you are aware of the exp[i(px+p^2(t)/2m)\hbar] ) setting p-p_0 to q and then coupling all terms...

Homework Statement Solve y' = (y^3)(t^2) for the initial condition y(0)=0 and state in which interval in 't' this solution exists. The Attempt at a Solution First I divided both sides by y^3 and then subtracted t^2 from each as well, -t^2 + y'(y^-3) = 0 then solved, (-t^3)/3 +...

Homework Statement A Ball is thrown upwards. What is its initial vertical speed? The acceleration of gravity is 9.8 m/s2 and maximum height is 7.2 m ,. Neglect air resistance. Homework Equations Vfinal squared = velocity initial squared + 2g times change in y The Attempt at a...

A stone released from balloon moving upwards with some constant velocity, the initial velocity of stone is same as the velocity of balloon with opposite sign, but how? What i thought is that the instant stone is released which goes upwards with balloon, stone which is going upwards would stop...

x=c_1\cos{t}+c_2\sin{t} is a two-parameter family of solutions of the DE x''+x=0 Find a solution of the IVP consisting of this differential equation and the following initial conditions: x(\frac{\pi}{6})=\frac{1}{2} and x'\frac{\pi}{6}=0 So x'=c_2\cos{t}-c_1\sin{t} x''=-c_2\sin{t}-c_1\cos{t}...

Homework Statement So it's based off of a track&field long jumper. Calculate the initial speed, v0, of a long-jumper where d=7.87 m. Assume a take-off angle of 21.4°, an initial height of the centre-of-mass of 0.920 m, and a final height of 0.460 m. So I use the range equation for...

Homework Statement According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy “Dizzy” Carlyle in a minor league game. The ball traveled 188 m (618 ft ) before landing on the ground outside the ballpark. Assuming the ball's initial velocity was 52 ∘...

Homework Statement So it's a projectile motion problem. I draw a graph showing the parabolic trajectory of the ball, with the start point at the origin. It's final x = 24.8m and final y = 0m Homework Equations We have three constant acceleration equations we use in my course: \vec{v}_{fx}...

Hey guys, i have read many posts on physics forums but this would be my first post. I am quite stuck so any help would be much appreciated. Homework Statement Use Laplace transforms to solve the initial value problem: f''(y) + 4f'(y) +8y = u(t-1) where y(0) = 1 and y'(0) = -1 Solve...

Homework Statement The range of a projectile is 483m, and it reached a maximum height of 65m. What were the initial speed and launch angle of the projectile? Assume the start and finish heights are equal. Homework Equations The Attempt at a Solution I just need a push in the...

I seldom review new electronics and new OS, but this one got to me. Please note that I'm not a rabid fan of anything. I have Macs, Windows, Android phone, and Apple iPads. I use them all. But I did like the IoS interface, which I found very intuitive and very easy to see, especially with my...

Apologies, this is most likely basic to most of you, and there are probably much better ways to go at this than I have. Homework Statement An 8mm wide cone of a hypothetical substance which does not melt, with a mass of 2.7 grams, is shot straight up at a 90 degree angle. Only accounting...

Hello, I'm doing an undergraduate introductory course in quantum mechanics, and I'm having a hard time understanding the interpretation. I've recently learned about the famous "Particle in a box" problem, in which we solve the time-independent schrodinger wave equation to get the energy...

I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just don't want it to seem like I'm...

I want to start out with a quick disclaimer, we had a 75 question homework packet assigned a few weeks ago with a few questions from every lecture and this first one is due tomorrow. I missed a lecture, so am completely lost on 3 questions from that lecture. Just don't want it to seem like I'm...

Homework Statement The question I am struggling with is the second version of a similar problem so to make it easier for me to receive assistance, I'll post both parts: Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an...

Homework Statement Solve the initial value problem: dx/dt = x(2-x) x(0) = 1 Homework Equations Problem statement. The Attempt at a Solution Based on the format, I attempted to solve the problem as a separable differential equation: ∫dx/(x[2-x]) = ∫dt Evaluating to...

Homework Statement A small rock is thrown vertically upward with a speed of 17.0m/s from the edge of the roof of a 30.0m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected. Homework Equations Acceleration...

I've tried a few different equations but I'm not sure how to start this problem. I just realized I'm looking for the initial velocity since the speed of the ball is constant. A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears...

Problem: Find the solution to the initial Value problem (differential equations)? y'=-y+e^-2x y(0) = 3 Attempt: y' -y = e^(-2x) ----- (1) Linear equation of first order of form y' + y p(x) = q(x) p(x)= -1 q(x) = e^(-2x) Find the integrating factor e^∫p(x) dx = e^∫ - dx = e^-x Multiply...

I have read the time line several times for the BB: http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang And I am unclear what were the initial ingredients at or before the 10-43 seconds. All I can get from this is high temperature which means high energy or high vibrational energy in...

Projectile Motion without Initial Velocity (Only time and angle given) Homework Statement A projectile is launched at an angle of 50° above the horizontal and it hits the ground in 12 seconds. a. Calculate the maximum height of the projectile. b. Find the range of the projectile...