Initial Definition and 1000 Threads

Homework Statement I am trying to solve the following: y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38 Homework EquationsThe Attempt at a Solution The right answer is: y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?

It is my understanding that to calculate the change of kinetic energy of an object that speeds up from vi to vf you use this formula: Change of kinetic energy = 1/2 * m * (vf2 - vi2) When the initial velocity is 0 m/s I have no problems, but let's say an object that weighs 2 kg speeds up from...

Homework Statement I am given (y^2 + y sin x cos y) dx + (xy + y cos x sin y) dy = 0, y(0) = π/2 . I need to solve this Homework EquationsThe Attempt at a Solution At this point they still aren't exact, so I gave up. I can't figure out what the problem is. Is it possible that I have to...

$\tiny{242.14.2}\\$ $\textsf{(a) Verify that y = $Cx^2+1$ is a general solution to the differential equation $\displaystyle x \frac{dy}{dx}=2y-2$}$ $\textsf{(b) Use part (a) to solve the initial value problem $\displaystyle x \frac{dy}{dx}=2y-2, \, y(2)=3$}$ $\textit{all new so kinda ??}$

Hi, I'm a bit confused regarding what steps to take to answer the following question: In 8 years, a new library is being opened. Expenses are estimated to be $52,000, payable at the end of each month. If all funds earn 14.4% compounded monthly, how much money needs to be invested today, to be...

Homework Statement If ##a_n## counts the number of ways to climb a flight of n stairs if one can take 1, 2, or 3 steps at a time, then ##a_n = a_{n-1} + a_{n-2} + a_{n-3}##. What are the three initial conditions? Homework EquationsThe Attempt at a Solution I would say that ##a_0 = 1## since...

Homework Statement Height - 15m Time when ball hits the ground after upward throw 3 s. I have been trying to find intitial speed with these formulas : d=v_initial*t-0.5*g*t^2 and v=v_initial+g*t Please help to understand how to find initial speed and after what time the ball is at 15m height...

Homework Statement If you know the acceleration of a car and its initial velocity, you can predict which of the following? A. The direction of the car's initial velocity B. The magnitude of the car's final velocity C. The displacement of the car D. All of the above Homework Equations I said...

Homework Statement A battery of internal resistance 0.50 Ω is connected (as shown below) through a switch S to a resistor X, which is initially at 0 °C. When S is closed, the voltmeter reading falls immediated from 12.0 V to 10.0 V. The reading then rises gradually to a steady value of 10.5 V...

Suppose that you take a thermometer outside where it is 100°. T(5min)=80° T(15min)=90° What is the initial temp of the thermometer? Given equation dT/d t= k(T-Te) Derived Equation ⌠(T-Te)^-1 (dT/dt)dt =⌠ kdt ln(T-Te)=kt + c T=ce^kt + Te so i basically got the answer by knowing c...

I have a problem where I need to figure out the initial velocity vector \vec{v_0} of a projectile, in order for it to land at the final position \vec{r_f} = x_f\hat{x} + y_f\hat{y} + z_f\hat{z}, from initial position \vec{r_0}. ___ The only knowns in the problem are \vec{r_0} and \vec{r_f}...

Homework Statement I have a block on an inclined plane (the angle is 40). The block is projected with an initial speed of 2m/s and μ=0.05. I need to find the time it takes the block to go up the inclined plane and return to the point it started out. Homework EquationsThe Attempt at a Solution...

Homework Statement Consider the system shown to the right. Particles 1 and 2 are fixed in place while particle three is placed at the location shown and released. Let’s look at the mechanics of q3, which has a mass of 3.00 X 10-5 kg. What will be the net force on q3?What will be q3’s...

Homework Statement A helicopter is flying in a straight line over a level field at a constant speed of 6.8 m/s and at a constant altitude of 9.4 m. A package is ejected horizontally from the helicopter with an initial velocity of 12.0 m/s relative to the helicopter, and in a direction opposite...

Homework Statement Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.745 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.115 m above the floor. With what initial velocity did Kit leave the cabinet if the...

Homework Statement A 2.0-kg cart collides with a 1.0-kg cart that is initially at rest on a low-friction track. After the collision, the 1.0-kg cart moves to the right at0.50 m/s and the 2.0-kg cart moves to the right at0.30 m/s .If the positive direction is to the right, what was the initial...

Hi I'm trying to solve a problem but I'm a bit confused about this part: Suppose you are walking at a speed of 2 m/s when you drop the ball that you were holding in your hands. Is the initial velocity 0 m/s? In the textbook it says that initial velocity for dropped objects is 0 m/s but that...

I seem to have missed the opportunity to post my questions on a related thread so I hope this is okay. First, a request. I have read on this forum that ["Singularity" is just shorthand for "the place where the math model breaks down and we don't know WHAT is/was happening".]. Since the wiki...

I've found online that the coherent state of the harmonic oscillator is |\alpha \rangle = c \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} | n\rangle where |n\rangle = \frac{(a^\dagger)^n}{\sqrt{n!}} |0\rangle and |0> is called the initial state. I've some code where I need to have this...

Use laplace Transform to solve this ode: So I got: sV(s)-V(0)-12V(s)=U(s+5) V(s)(s-12)=U(s+5)+1 V(s)=[U(s+5)+1]/(s-12) Now to go back to time domain with Inverse Laplace Transform...My question is, how to transform U(s+5)/(s-12)? Any help? Thanks guys

Homework Statement Disk P (inertia 0.41 kg ) moves at an unknown velocity across a low-friction horizontal surface and collides with disk Q (inertia 0.75 kg ), which is initially at rest. After the collision, the two (now slightly dented) disks move apart without spinning. Velocity information...

Homework Statement Homework Equations Fluid in rotation The Attempt at a Solution This exercise is quite different from the classic one of fluidi in rotation. Before rotation starts the height in one branch is bigger than in the other, so I do not really know how to approach the problem...

Hi I have a pipe Which has constant heat flux from walls. I need to get pressure drop (dP) and temperature rise (dT) in outlet as results. I know the velocity inlet, but don't have pressure inlet and tempreture inlet. Would fluent be able to solve the modeling and give me dP and dT? I emphasize...

Say we start with a wavefunction inside a harmonic potential well, such that the initial ##\psi(x)## is confined to a central region much smaller than the ground state (hence ##V(x)\approx0##).. and the expectation Kinetic Energy is equal to an energy eignenvalue ##E_n## of the system. Starting...

Homework Statement Alex Morgan is going to kick a soccer ball into the Canadians goal during the 2015 world cup. Alex kicks the ball straight at the goal from 20.0 m away, and it launches off the ground at an 33.3 degree angle. Assume the goalie is busy faking an injury and ignore air...

The Schwarzschild equation of motion, where coordinate length is differentiated by proper time is as far as I know r''(t) = -\frac{G\cdot M}{r(t)^2} + r(t)\cdot{\theta}'(t)^2 - \frac{3\cdot G\cdot M\cdot{\theta}'(t)^2}{c^2} {\theta}''(t) = -2\cdot r'(t)/r(t)\cdot{\theta}'(t) Now the question...

Homework Statement A bobsled glides down a hill with an acceleration of -4.5 m/s If it stops after 5 s, what was its initial velocity? 2. Homework Equations i know vf(final)= v + at The Attempt at a Solution i multiplied -4.5m/s by 5s and i got the correct answer the only problem is the...

Homework Statement A 1350kg car traveling at 72km/h collides with a slow-moving car of mass 1650kg, also initially traveling south. After the collision, the velocity of the 2 cars together is 24km/h. Determine the initial velocity at which the second car was travelling. Given: m1=1350kg. vi1 =...

Homework Statement A 1000kg car is moving at 25ms when a net force of 200N acts to slow the car. This force acts while the car moves through a distance of 300m. Find the new speed. Homework Equations Kinetic Energy equation v2=u2+2as The Attempt at a Solution Attempted the use of Kinetic...

Warren falls over his tackle box and lands in a canoe 0.95 m below the side of the dock. Warren's mass is 70 kg and the canoe has a mass of 72 kg. Warren and the canoe move 1.73 m away from the dock in 1.005 seconds. relating equations are Vi = Vf - at v = d/t A = change in velocity/time...

Is it possible to solve for the initial speed of projectile hitting a target given that we know the direction (vector) that it is released at and the point on a the surface that it is hitting? If so how would you go about finding an equation to solve for this? I realize that this is a...

Homework Statement 40kg girl and 8.4kg sled are 15m apart on the surface of a frozen lake. By means of a rope, girl exerts a horizontal force of 5.2N on the sled, pulling it towards her. How far from the girls initial position do they meet? Homework Equations f=ma The Attempt at a Solution I...

Homework Statement Calculate the number of white dwarf, neutron star and black holes the galaxy will have after 5Gyr of evolution. M<8(solar mass) for white dwarf 8(solar mass) < M < 40(solar mass) for neutron star M > 40(solar mass) for black hole Initial mass function is ξ(M) = AM-s...

In a gravitational field you can put a particle and it is immediately subject to a force that tries to accelerate it. But in a curved spacetime notion if you put a particle it has no reason to move. Right?

1. Homework Statement Ok so, for part b ii) The solution did this : 1/2 (0.065) (2π /0.3)2 (1.5 x 10-2)2, which is the KE of the mass when its speed is max. But why do they calculate the energy when it is at its equilibrium position where its speed is max? I assume that the energy before...

Homework Statement An athlete can cover 3.0 m for a standing long jump. Assuming that this athlete jumps at an angle of 45 degrees to the horizontal. calculate the speed at which the jumper can launch herself from a standing start. Assume g =10 ms^-2 and no air resistance Assume that horizontal...

I am doing a lab in my senior physics class (IB HL Physics 3-4) and I am very confused about a relationship that I found. For my experiment I dropped a racquetball from different heights and then used video analysis to find the height of the ball on its final bounce. I used this data to...

Homework Statement Given an initial value problem: ##x'(t)=f(t,x)\,,x(t_0)=x_0## Use centered finite differences to approximate the derivative, and deduce a scheme that allows to solve the (ivp) problem. Homework Equations For centered finite differences ##\displaystyle\frac{dx}{dt} \approx...

Homework Statement how to know that the nozzle increases the velocity of water by 6 times? it's not given ... and no data for initial velocty given Homework EquationsThe Attempt at a Solution

Homework Statement What initial velocity has to have a ball at the height h=1m in order to sink in the water to depth of s=4m? How long is the motion of a ball through water? A ball is made of material that has density \rho=770 kg/m^3. Surface tension and friction are negligible. Homework...

Homework Statement The scenario is a pendulum of length l and mass m2 attached to a mass of m1 which is allowed to slide along the horizontal with no friction. The support mass moves along in the X direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After...

***Sorry I meant to say finding time when you have initial velocity and position*** 1. Homework Statement A test rocket is launched by accelerating it along a 200.0-m incline at 1.36 m/s2 starting from rest at point A (the figure (Figure 1) .) The incline rises at 35.0 ∘ above the horizontal...

Homework Statement A football started on the ground 64 yards from the base of the goal post and barely clears the 10 ft high bar. The initial trajectory of the football was 43 deg above the horizontal. What was its initial speed? Homework EquationsThe Attempt at a Solution (vf)^2 = (vi)^2 +...

My brother and I were having an argument so I decided to make an account on this forum. Say you were to lurch you hand forward while firing a pistol. Would that affect the max velocity of the bullet?

1. Problem I have a horizontal cylinder with a ball in it. What must the initial pressure be to launch the ball at Z velocity? 2. Attempt P = F/A A = Surface Area(Cylinder) - 1/2 Surface Area (Ball) = (2πrh) F = m*a U = - ∫ F dx U = 1/2 mv^2 at x = h ∫ a dx = -1/2mv^2 / m at x = h Z =...

This question is on space and projectiles. It is about comet 67P/ Churyumov-Gerasimenko and the Rosetta/ Philae lander. Question: 67P has a gravitational field strength of 5.2x10^5 N/Kg. After Philae bounced it took 1 hour 50 minutes to reland. Calculate the initial velocity of Philae. Does this...

Homework Statement A German U2 rocket from WW2 had a range of 300km, reaching a maximum height of 100km. Determine the rocket's maximum intial velocity. X component variables: di=0, df=300, a=0, time=9, vi=? Y component variables: a=-9.8, vf=0, vi=?, di=0, df=100, displacement=100, Note: For...

I am not a scientist, but as a hobby I am summarizing different initial condition theories, specifically, eternal inflation, LGC, cyclic, and bounce theories. I need a completion time ATB where all theories produce an identical plasma. The plasma then enters the big bang process of expansion...

Homework Statement A skydiver is jumping out of an airplane. During the first few seconds of one jump, the parachute is unopened, and the magnitude of the air resistance acting on the skydiver is 251N. The acceleration of the skydiver during this time is 5.96 m/s^2 [down]. Calculate the mass of...

Homework Statement I have the solution to the heat equation, with the BC's and everything but the IC applied. So I am just trying to solve for the coefficients, the solution without the coefficients is $$u(x,t) = \sum_{n=1}^{\infty} A_n\sin(nx)e^{-n^2t}$$ If the initial condition is ##u(x,0) =...