Initial Definition and 1000 Threads

Hello! (Smile) I want to find the exact solution of the recurrence relation: $T(n)=2T(\sqrt{n})+1$.$$m=\lg n \Rightarrow 2^m=n \\ \ \ \ \ \ \ \ \ 2^{\frac{m}{2}}=\sqrt{n}$$ So we have: $T(2^m)=2T(2^{\frac{m}{2}})+1$ We set $T(2^m)=S(m)$, so we get: $S(m)=2S \left( \frac{m}{2}\right)+1$...

Homework Statement Equation for the time of a free fall with an initial velocity? Homework Equations √ (2 ⋅ h / a ) The Attempt at a Solution Is it √ (2 ⋅ h / via )Thanks for the help :)

How to find the Initial guess for Newton method with high accuracy ?? Is there a way rather than using mean value theorem [which is used to test whether there is a solution on a closed interval to the equation] ?

Homework Statement A UPS delivery man pushes a 5kg box (A) along a smooth surface where the coefficient of kinetic friction, [µ][/k], is equal to 0.20. The box slides for 1.5m before colliding with a 3kg box (B). The boxes then move together as one unit on a rough surface with [µ][/k]= 0.9 for...

Homework Statement A motorcyclist wants to jump 20 cars placed side-by-side, making the jump 30m long (coming back to the initial height). Assume that the ramp is placed at an angle of 30 degrees from the horizontal. a. Calculate the initial velocity required to make the jump. b. Assuming the...

I think I more or less understand how a gyroscope precesses--at least mathematically and in terms of torque/angular momentum. My question here is: how does the gyroscope start precessing in the first place? The external forces on the center of mass are entirely vertical. Given that Newton's...

Hi, I'm new here and I'm having trouble with a question. 1. Homework Statement A 20.0-kg curling stone is released at the hog line and moves 28.35 m [W] to sit on the button and score a point. If the coefficient of kinetic friction between the stone and the ice is 0.00200, what was the...

Hello, I have two different discrepancies to this system: a) How and when is possible to have more solution of differential eq. or their system for same initial problem? For example this is happening in following system. It is written about this system: "Different value of constant \dot{M}=4\pi...

If a projectile is thrown at an angle of 60o and it's initial speed is 30m/s, find the maximum height, time used for the ball to reach the ground, the horizontal range the ball reached from starting point, and the final velocity. So can i use 30m/s as the initial velocity?

Hey, I need help with a lab I'm doing in class. The goal is to hit a target on the ground by shooting a bullet from a toy gun. Our distance from the target will be assigned to us by our teacher and I need to calculate the initial velocity of the gun and then hit the target by only changing the...

Homework Statement The original superman leaps into the air to land on an 85.5 m high building. What was his intial velocity? d = 85.5 m v2 = 0 v1 = ? a = 9.8 m/s2 (I'm not sure about this one so I just used acceleration due to gravity) Homework Equations v2 = v1 + 2ad (?) The Attempt at a...

Disregarding air resistance, how could you find an accurate number for the initial velocity of a toy gun?

Homework Statement A Rail car with a mass= 27000kg's moving at 4m/s collides with another rail car with mass 80,000kg that was moving towards the first. After the collision, both cars come to a complete stop, what was the initial speed of the second rail car? Homework Equations...

Homework Statement Determine the exit speed(initial velocity) of a marble exiting a launcher shot from a table. The height of the table, distance of the x component and the time can be measured. t=? Vi=? Vix=? Homework Equations d= vi * t + 0.5*g*t^2 Vi^2=Vix^2*Viy*2 The Attempt at a Solution I...

1)The breech and barrel of a field gun have a total mass of 453.6kg. The recoil of the barrel is controlled by resistance forces from a buffer and recuperator, these forces are given by: Buffer force=71000/(s+1), recuperator force= P+ 4380s. (both are in Newtons). s is the recoil of the barrel...

Homework Statement Neutral metal sphere A, of mass 0.10kg hangs from an insulating wire 2.0m long. An identical metal sphere B, with charge -q, is brought into contact with sphere A. The spheres repel and settle(a picture just imagine a right angle triangle with 2 objects A and B at the...

Homework Statement Two small spheres with charges 1.6*10^-5 C & 6.4*10^-5 C, are 2.0m apart. The charges have the same sign. Where, relative to these two spheres, should a third sphere, of opposite charge 3.0*10^-6 C, be placed if the third sphere is to experience no net electrical force? Do we...

This problem was given verbally during a class period, so I will set it up in my own words. A bullet (.012kg) is fired at a block (.800kg) hanging on a strong, massless string of length 1.6m. After the collision the bullet is embedded in the block. When the block is .8m above its original...

Homework Statement If y = y(t) is the solution of the initial value problem y' + (2 t + 1) y = 2 cos(t) y(0) = 2 What is y''(0)? Homework EquationsThe Attempt at a Solution Since this is a first order linear, I started out by finding the integrating factor so I can find what y is, and then...

Homework Statement An object is thrown from the ground into the air at an angle of 30 degrees to the horizontal. If this object reaches a maximum height of 5.75m, at What velocity was it thrown? a= -9.81 m/s h= 5.75 m I know that velocity is the one that I need to solve but I'm kinda finding...

Homework Statement Estimate the average force exerted by a shot-putter on a 7.0-kg shot if the shot is moved through a distance of 3.0m and is released with a speed of 10m/s . Homework Equations F=ma Maybe the Five Equations for constant acceleration? The Attempt at a Solution So my guess is...

Homework Statement y'' + 4y = t2 + 6et; y(0) = 0; y'(0) = 5 Homework Equations The Attempt at a Solution So, getting the general solution, we have r2 + 4 = 0, so r = +/- 2i So the general solution is yc = sin(2t) + cos(2t) I then used the method of undetermined coefficients to figure that...

Homework Statement I'm trying to create a problem for my physics standards that is hard. I gave myself a ball being pushed down a carpeted decline at 24° from the horizontal. The balls starts with an initial velocity of 1 m/s and ends the 6 meter decline at 5 m/s. I want to find the applied...

Homework Statement I'm taking grade 12 U physics and I'm having a really difficult time understanding the answers given compared to the answers I arrive at. For example: The question reads: A rock was thrown horizontally from a 25.0 m high cliff and landed 15.0 m from the base of the cliff...

when i use this MATLAB code but with rectangular pulse shape instead of chirped pulse i didn't get the predicted output , so is there a limitation with this method in case of rectangular pulse or the MATLAB code is wrong...

Homework Statement You are riding in a hot air balloon at an altitude of 167 meters traveling at a horizontal speed of 24 m/s. If you fall out of the basket, how long will it take you to hit the ground? How far will you travel horizontally in this time. What is your total speed when you hit the...

Homework Statement A falling stone takes 0.33 s to travel past a window 2.2 m tall. From what height above the top of the window did the stone fall? Express your answer using two significant figures. Homework Equations Kinematic Equations ~ X= Vi (time) + .5gt^2 Vf^2 = Vi^2 + 2gxThe Attempt...

Homework Statement Using the energies, determine from which initial energy level (n) the electrons decayed when it emitted photons at each of these wavelengths. Homework Equations E = - \frac{ me^4 }{ 8\epsilon_0^2h^2 }\frac{ 1 }{ n^2 } Delta E = E_f-E_i= - \frac{ me^4 }{ 8\epsilon_0^2h^2...

Homework Statement You’re 5.00 m from the left-hand wall of the house shown in the drawing, and you want to throw a ball to a friend 5.00 m from the right-hand wall. You throw the ball so that at the peak of its trajectory it just clears the top of the roof...

Homework Statement A projectile with initial velocity u making an angle A with the horizontal. Find the time t when the velocity of the projectile becomes perpendicular to its original velocity.Homework Equations v = u + at s = ut + 1/2at^2 v^2 - u^2 = 2as[/B] The Attempt at a Solution I have...

a high diver leaves the end of a 5.0 m high diving board and strikes the water 1.4 s later, 2.8m beyond the end of the board. Considering the diver as a particle, determine the following: a) her initial velocity & angle above horizontal. b) max height reached above water c) final velocity as...

The problem is from Adam's Calculus (7th Ed). It is an initial value problem, and I solved it: \begin{cases} y'=\frac{3+2x^{2}}{x^{2}} \\ y(-2)=1 \end{cases} \\ \implies y=-\frac{3}{x}+2x+\frac{7}{2} I can see that the solution is not valid for x=0, but the book says that the solutions is...

Homework Statement If you want to use a catapult to throw rocks, and the max range is 0.67 km, what initial speed must the rocks have as they leave the catapult?Homework Equations v=Δr/Δt The Attempt at a Solution I sketched a graph of the projectile trajectory with the desired range on the...

Homework Statement Hello all, I'll try to keep this as short as possible! :) I won't include the particular values we were given, just so I still have to do something for this part. It shouldn't matter too much, I believe. My team and I are acting "car crash investigators" for the purpose...

"If the height of the water slide is h = 3.2m and the person's initial speed at point A (at the top of slide) is 0.54m/s, at what location does the swimmer splash down in the pool?" I saw a thread with the same question back from 2005 but it is now closed. I understand that you have to use...

Homework Statement x \frac{du}{dx} \ = \ (u-x)^3 + u solve for u(x) and use u(1) \ = \ 10 to solve for u without a constant. Homework Equations The given hint is to let v=u-x The Attempt at a Solution This equation is not separable and the book wants me to make it separable...

Homework Statement For archery practice, a knight's squire drops sandbags from a 12.0 meter tower. At exactly the same time the sandbag is dropped, the knight shoots an arrow up at the sandbag from the base of the tower. If the arrow strikes the sandbag at exactly 1.1 seconds, calculate a)...

Does anyone know how the mathematics/formulae of SHM (say a particle in a force field, with the standard a=-d) changes when the particle is given an initial velocity independent of the force causing SHM? For example in 1D say we have a graph of acceleration-displacement in the standard form...

Do you think we will ever be able to create a simplified computer simulation of the universe using the cosmic microwave background as the initial state that would generate the true locations of galaxies or at least galaxy clusters, and then be able to find our own galaxy or galaxy cluster within...

Hi all, I have been given a projectile motion problem, where a ball is launched from a catapult. The range, maximum height and the launching angle is known. The range is 2.32m, the max. height is 1.26m and the launching angle is 35° from the horizontal. The projectile flight goes for 1.125...

A car drives at constant velocity on a road. As it comes near a stop sign, the driver brakes, which makes the car decelerate at 4.7 m/s/s. If the car traveled 9.8 METERS while the driver was braking, what was the starting or initial velocity just when the driver was hitting the brakes? I...

Homework Statement Ball A is thrown straight upward and returns to its original level in 2 seconds. Ball B is thrown at a 40 degree angle above the horizontal and also returns to its original level in 2 seconds. What is the initial speed of each ball. Homework Equations ΔV=at...

home run that was estimated to have landed 180 metres from the home plate and to have reached a height of 21.3 metres. Calculate the initial velocity of the ball. u^2=v^2-2as t=? u=? v=0 s=180 a=g= -9.8 u^2= √0^2-2x-9.8x180 u= 59.9 m/s am I using the right equation for...

Hi all. Say we have a background inflaton field ##\varphi## and that we've integrated the background equation for ##\varphi##, ##H(\eta)##, and ##a(\eta)## up to the number of e-folds of inflation corresponding to ##\epsilon = 1## in the slow-roll parameter. We then wish to solve for the ##k##...

For the following problem \frac{dw}{d\theta}=\theta w^{2}sin(\theta^{2}), w(0)=1 I am not able to obtain the solution w=\frac{2}{1+cos(\theta^{2})} Can anyone point out my mistake? I have attached my working out in a picture format below (may need to enlarge it) thanks

did i do these two questions right? #1 $y'=xe^{- \sin\left({x}\right)}-y \cos\left({x}\right)$ $y'+y \cos\left({x}\right) = xe^{-\sin\left({x}\right)}$$I(x)=e^{\int \ \cos\left({x}\right)dx}$ $\int \...

Homework Statement Hello, An object moves at constant speed in a horizontal surface. Suddenly, a ramp comes along its way. The object starts to climb such ramp. Due to this, the object starts to lose speed. At certain distance, the object loses all of its speed. I want to calculate the value...

Homework Statement Use Newton's method with x1 = 1 to find the root of the equation x3 - x = 1 to correct six decimal places. Do the question again with x1 = 0.6 Do the question again with x1 = 0.57 You probably need to do it in an excel sheet. With each try, it takes longer to...

Homework Statement A disk rotates with constant angular velocity \omega. Two masses, m_A and m_B, slide without friction in a groove passing through the centre of the disk. They are connected by a light string of length l, and are initially held in position by a catch, with mass m_a at a...

Homework Statement An 80-kilogram man jumps off a raft that weighs 100 kg. His initial velocity from jumping is 7 meters per second. Assuming that the friction resistance of the water is zero, the velocity of the raft after the man jumps will be? Homework Equations Vf^2= Vi^2 + 2aD...