Initial Definition and 1000 Threads

Homework Statement Solve: \frac{\partial H}{\partial t} = -4\kappa H^{2} With initial condition: H(0) = 1/L^{2} To find: H(t) = \frac{1}{4\kappa t + L^{2}} 2. The attempt at a solution I tried using Taylor series expansion such that: H(t)\approx H(0)+t\frac{\partial...

Homework Statement Find a continuous y(t) for t > 0 to the initial value prob: y'(t)+p(t)y(t)=0, y(0)=1 where p(t)=2 for 0 < t < 1 p(t)=1 for t > 1 and determine if the soln is unique. The Attempt at a Solution By standard ODE techniques I arrive at y=\exp(-2t) for 0 < t < 1 y=\exp(-t)...

Homework Statement A person wants to shoot a rocket off of a mountain 3.26 km high so that the rocket, when shot at 31.3° above the horizontal from the very top of the mountain, lands at the foot of the mountain 9.37 km (horizontal distance) away. What initial speed must the rocket have...

Homework Statement According to the range equation (see below), what angle would give teh maximum range for a given initial velocity? Mathematically explain your hypothesis. Homework Equations The equation given in our book for range: R=(V_{o}cos\Theta)*(2V_{o}sin\Theta)/g...

Homework Statement Exact question: A hobby rocket reaches a height of 35m and lands 259m from the launch point. What was the angle of launch? We know... Xmax = 259m Ymax = 35m Xo and Xmax are at equal y values, or heights, 0 in my chosen coordinate system Homework Equations 1)...

Homework Statement 1. To use Euler midpoint method to find an approx value to y(0.1) using a step size 0.1 2. To use integrating factor method to find exact value of y(0.1) 3. Determine the global error ( min 5 decimal places) Homework Equations f(x,y) = x+y, y(0) = 1.35 The...

Homework Statement Let f(t) be the solution to the initial value problem 2t(dy/dt)+y=t^4 with f(0) = 0 find f(t). Homework Equations The Attempt at a Solution I tried to do this by separating variables but that hasn't gotten me very far. I don't know if I can do it by doing...

Homework Statement A kicker is attempting a field goal from 50 m from the goal posts, which are 3.44 m high. He can kick the ball with initial speeds of 25 m/s. Ignoring air resistance, within what angular range must he kick the ball to score? Homework Equations Pf = Pi + Fnet*t And any...

Homework Statement Compute the initial upward acceleration of a rocket of mass 1.2 multiplied by 10^4 kg if the initial upward force produced by its engine (the thrust) is 2.7 multiplied by 10^5 N. Do not neglect the gravitational force on the rocket. Homework Equations F = ma...

Homework Statement The first stage of a Saturn V space vehicle consumes fuel at the rate of 47400 kg/s, with an exhaust speed of 2820 m/s. The acceleration of gravity is 9.8 m/s2 . Calculate the thrust produced by these en- gines. Answer in units of N. (part 2 of 2) 10.0 points Note...

Hey guys, I was wondering how to find the initial velocity of a ball going up with only the time. The time I have is 3.37, would I use the formula: dy=1/2(a)(t)^2 to find the initial velocity? I got 33.026 m/s but I don't think that's right.

1. Homework Statement For a certain experiment, R-410a vapor is contained in a sealed glass tube at 20°C. It is desired to know the pressure at this condition, but there is no means of measuring it, since the tube is sealed. However, if the tube is cooled to −20°C small droplets of liquid...

Hello Everyone, Is there a list online somewhere of which variable values are 0 and why (conceptually), based on initial conditions? Like I know that for a system at constant volume, w=0. I am looking for a list for the other effects like isothermal, adiabatic, what does pressure= if there is...

Homework Statement A ball is hit from the ground with an angle of 36 degrees above the horizontal. The ball hits a target 30m ahead and 4m above the ground. Find the initial velocity of the ball. Homework Equations Vavg = Δd/Δt aavg = Δv/Δt Δd = voΔt + 1/2aΔt2 The Attempt at a...

Homework Statement A stone is projected vertically with a initial velocity u. Another stone projected from the same position verticaly with same velocity u after time t. Find the velocity of both stones when they meet together & time taken to meet. Homework Equations S = ut + 1/2 at2...

Homework Statement haha, so hopefully my last question for the night! Find the initial velocity, when the object is shot at 70 degrees and took 6.5s to land. (hint: look at the y direction first this time) (For more information regarding my question, visit my earlier question from tonight...

Homework Statement An object is shot (from a cannon) at an angle of 33 degrees and landed 85 m away. Calculate the magnitude of the initial velocity (Hint:Look at the x direction and solve for Vox) Homework Equations Other questions I must answer. If you have time, help with these would...

Homework Statement Solve the initial value problem (y+e^-y)y'=sinx subject to y(pi)=0 Homework Equations The Attempt at a Solution I'm not quite sure what to do with this one. I've scanned through my book and could find no similar problems in what we've done so far. I tried to...

Homework Statement To Find initial velocity, given final velocity, and displacement on Y axis. Hello. I've spent four hours trying different solutions to this following problem, none of which have worked. I've just started my undenominated science degree, and since I havn't started lectures...

1. A home run is hit such a way that the baseballjust clears a wall 27 m high located 147 mfrom home plate. The ball is hit at an angleof 37◦ to the horizontal, and air resistance isnegligible. Assume the ball is hit at a heightof 1 m above the ground.The acceleration of gravity is 9.8 m/s2...

The problem: The record distance in the sport of throwing compats is 81.1m. This record toss was set by Steve Urner of the US in 1981. Assuming the initial launch angle was 45 degrees and neglecting air resistance, determine a) the initial speed of the projectile and b) the total time the...

Homework Statement 1. A projectile is launched at angle(theta) relative to the horizontal (see the figure below). The initial height of the projectile above the surface of the table is h, and it hits the table at distance (delta)x from the launch point. Find the launch speed vi of the...

Problem: Starting co-ordinates S 45° 50.061 E 170° 27.079 A catapult stationed at the above coordinates will hit the castle, if it shoots at maximum range (X meters) at 48ºtrue. Assume equal initial and final elevation for the projectile’s trajectory, and the projectile’s initial velocity is...

Homework Statement A ball thrown into the air lands on the same horizontal level, 38 m away, and 3 s later. Find the magnitude of the initial velocity. Homework Equations x = vox The Attempt at a Solution I just plugged the x distance which is 38m and the time which is 3s into...

You shoot an arrow into the air. Two seconds later (2.00 ) the arrow has gone straight upward to a height of 25.0 above its launch point What is the initial velocity or the formula I would use to find

Homework Statement An accelerating lab cart passes through two photo gate timers 3.0 m apart in 4.2 s. The velocity of the cart at the second timer is 1.2 m/s (4 marks) a.) What is the cart’s velocity at the first gate? b.) What is the acceleration? Homework Equations v = vi + at Vaverage...

Homework Statement Knowing that snow is discharged at an angle of 40 degrees, determine the initial speed, v0 of the snow at A. Answer: 6.98 m/sHomework Equations The Attempt at a Solution I have found the x and y velocity and position formulas. Now since I don't know time, should I...

Homework Statement Help! I have no idea where to begin for this! You are driving along a straight section of roadway (x-axis). You spot a police officer and apply the brakes, slowing down at a constant rate. Your positions (in meters) at successive time intervals of 0.465 s are tabulated...

Initial Velocity and Acceleration--Please Help! Homework Statement You are driving along a straight section of roadway (x-axis). You spot a police officer and apply the brakes, slowing down at a constant rate. Your positions (in meters) at successive time intervals of 0.515 s are tabulated...

The world's highest fountain of water is located, appropriately enough, in Fountain Hills, Arizona. The fountain rises to a height of 560 (5 feet higher than the Washington Monument). What is the initial speed of the water

How do u find the initial speed of an object

Homework Statement I need to set up the mathematical formulation of the following heat conduction scenarios: a) A slab in 0\le x \le L is initially at a temperature f(x). For times t>0 the boundary at x=o is kept insulated and the boundary at x=L dissipates heat by convection into the...

Hey guys, I'm looking to calculate the initial velocity of a large object sliding to a stop over a surface. This is easy without the drag force of the air, but I'd like to include that to prove a point in my research. As a quick background, I haven't done a differential equation in over a...

Homework Statement In problem 11, determine by inspection at least two solutions of the given initial-value problem. Homework Equations 11. dy/dx = 3y^(2/3) , y(0)=0 The Attempt at a Solution I can't figure out what they mean by inspection, I have no examples to go off from...

Let's consider a second order differential equation f(x,\dot x,\ddot x,t)=0 and let's suppose that f satisfies all the conditions of the Cauchy Theorem, i.e. f is such that the equation above with the initial conditions x(t_0)=x_0\qquad\dot x(t_0)=v_0 has an unique solution in a...

Homework Statement Electron shot in x direction with V_o=3.5*10^6 and is accellerated thru parallel plate capacitor with potential difference of 70V. after it travels on the x-axis for 5 mm what is its total field the electron produces? including magnetic and electric. Show direction and...

Hi all, I am trying to work out the initial velocity of dry air, through a 3" opening in a pressurized tank (150 psi). I thought I should use Bernoulli's eq. as a start: P=1/2*rho*V^2 by changing the formula to give velocity, V = sqrt(P*2/rho) Then I realized there was no time value in...

1) (dy/dx) = (1) / ( 2√x ) + 10 , y(1) = -1 2) (d^(2)r / dt^2) = ( 4 / t^3 ) ; (dr/dt) | t=1 = -5, r(1)=5 ... i have no idea where to start. what are the steps needed to figure out the answer...can someone please solve this for me! t thank you so much.

I'm modeling a physical system described by a second-order ODE with LOTS of parameters. Using SciLab, I sucessfully implimented the model using a while loop with time. Because of the loop structure, every time I called the DE solver (ode), I updated the intial conditions for the current...

Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...

Please verify my answer. Homework Statement Use Newton’s method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) x^5+2=0, x_1=-1 Homework Equations The Attempt at a...

Homework Statement Hi, I need to figure out the initial velocity if an object of 1400 kilograms is subjected to a friction coefficient (sliding friction) of 0.4587 for 75.6 metres, and its final velocity after being subjected to that friction is 23.05 metres per second. How do I go about this...

Homework Statement Let u(x,t) be the solution of the following initial value problem for the nonhomogeneous wave equation, u_{x_1x_1}+u_{x_2x_2}+u_{x_3x_3}-u_{tt}=f(x_1,x_2,x_3,t) u(x,0)=0 and u_t(x,0)=0 x\in\Re^3 , t>0 Use Duhamel's Principle and Kirchoff's formula to show that...

The total energy of a particle is given by: E_{tot} = 2 \dot{x}^{2} - cos(\frac{1}{2} \pi x) and I'm told that the particle passed through the point x=1 [m] with a velocity of \vec{v}=-\frac{1}{2} \hat{x} [m/sec]. I'm required to find the maximum velocity of the particle during its motion...

Homework Statement An 8.00 g bullet is fired into a 160 g block that is initially at rest at the edge of a table of 1.00 m height. The bullet remains in the block, and after the impact the block lands d = 2.2 m from the bottom of the table. Determine the initial speed of the bullet...

Homework Statement A juggler throws a ball straight up into the air with a speed of 10 m/s. With what speed would she need to throw a second ball half a second later, starting from the same position as the first, in order to hit the first ball at the top of the projectory? My problem is I am...

Homework Statement A rock climber stands on top of a 50-m-high cliff overhanging a pool of water. He throws two stones vertically downward 1.0 s apart and observes they cause a single splash. The initial speed of the first stone was 2.0 m/s. a) How long after the release of the first stone...

Homework Statement A stone is dropped off a bridge 50m above the water. Exactly 1s later another stone is thrown down and both stones strike the water together. What must the initial speed of the second stone have been? ohh I am sorry but i have no idea please help me out here thank you...

I wonder where I work, 3-phase ind. motor with 80 ohms resistance per phase from the manufacturer was re winded and the new resistance per phase was 89 / 90 / 94 Ohms in the 3 phases. when the motor was put back, it burnt within few hour, why was this?

My senior design project is to build a hybrid motorcycle. Using a hydraulic engine we are converting the breaking power of the motorcycle into stored energy for use when the motorcycle accelerates from a stop. The question is how to find an appropriate initial acceleration. The acceleration...