Balls Definition and 541 Threads

Homework Statement Let x,y be in R^k, |x-y|=d. Prove there are an infinite number of solutions to |z-x|=|z-y|=r when 2r>d. Homework Equations I have done this problem for 2r=d and 2r<d. For 2r<d, the triangle inequality works nicely. For 2r=d, the equality gives me additional...

Homework Statement Prove that the sum B_r(\alpha)+B_s(\beta) is exactly the ball B_{r+s}(\alpha+\beta) Homework Equations open ball B_r(\alpha) of radius r about the center \alpha is \left \{\epsilon: |\alpha-\epsilon|<r\right\} The Attempt at a Solution I have difficulty of proving...

Homework Statement A juggler throws a ball at 10m/s and it takes 0.24 seconds to reach the ceiling which is 2.4m high. As this ball reaches the ceiling he throws a second ball also at 10m/s. How long after 2nd ball is thrown do they pass Homework Equations maybe just too late but I am...

Hi all, I need help with the following problem: The urn contains 5 black and 8 red balls. You close your eyes and remove balls from the urn one by one without replacement. What is the probability that the last ball is black? This looks to me like it is a hypergeometric distribution...

Hi, i have a couple of problems that I am not sure about (i get the wrong answer for particular cases because the probability add up to more than 1) say you have 50 balls and 20 bins, you throw all 50 balls into the bins, with equal probability of a ball landing in each bin 1. what is the...

Does anyone know how to solve this game: http://www.puzzlechoice.com/pc/IQ_Gamex.html as in the highest and second hisghest scores. I am sure there's group theory somewhere, but I never got it... :-/

When you throw a ball, why does it spin? Does it have to do with the air resistance? Obviously, you can spin it when you throw it, but it seems to spin even if you just "push" it up. Is it that I'm just not being precise here? Is this related at all to why it's easier to balance on a bike...

HI, sorry about the english can you help me with this question? box initially contains 10 black balls and 10 white balls. The following experiment is repeated indefinitely 20 times : A ball is drawn from the box; if the ball is black it is put back in the box, otherwise it is left out. what...

Hi folks, I'm imagining the following situation: Two balls lie at the base of a hill, side by side, not touching. One is larger and masses more than the other. They are made from the same material. Suddenly, they both experience the same acceleration towards the hill. They don't ever come...

We are demolishing some old cryogenic tanks and inside them were large metal balls. The metal is very hard and dense and has a yellowish tint. The tanks are large upright and cylindrical. Need information on the purpose of the balls and what material(s) they might be made of. I would...

Homework Statement Two balls are thrown with equal speeds from the top of a cliff of height h. One ball is thrown at an angle of α above the horizontal. The other ball is thrown at an angle of β below the horizontal. Show that each ball strikes the ground with the same speed. (Do this on...

Two balls problems...please help! Homework Statement Two particles are thrown vertically upwards along the same line with the same initial velocity u=30m/s, but at different times. The second particle is thrown t seconds after the first. What should be the minimum value of t so that the...

I have 5 different types of balls made out of different materials, all similar but not identical in weight, and all of the the same size. What is the best mechanism to sort these by weight? I can use any mechanical device to sort these balls, such as seesaws, etc. What is the most efficient way?

Homework Statement Two balls are thrown with equal speeds from the top of a cliff of height h. One ball is thrown at an angle of alpha above the horizontal. The other ball is thrown at an angle of beta below the horizontal. Show that each ball strikes the ground with the same speed, and find...

Homework Statement Ball 1: 3kg, 7 m/s initially Ball 2: 4kg, V m/s initially Ball 3: 5kg, 10 m/s initially Find V if the system collides inelastically and moves off at 2 m/s at 5 degrees above the horizontal. Homework Equations p + p = p + p (in both x and y directions) The...

Homework Statement You have an urn that contains n balls labeled with the natural numbers {1,2,3,...,n} and you extract n balls from the urn (with the condition that a ball may not be returned to the urn once drawn). You have to determine the distribution of X=(X1,X2,...,Xn), where Xk is...

Billiard Balls with "English" I was just watching the classic episodes of The Mechanical Universe, and one scene explained how billiard balls rebound at right angles. I understand that. But I wonder how http://en.wikipedia.org/wiki/Glossary_of_cue_sports_terms#English" causes the effects it...

Homework Statement I have 2 equally charged pith balls suspended by a string repelling each other at a 28 degree angle. I know that Tension, Gravity, and the electostatic force are all acting. I found tension by creating a force diagram. T= cos14mg. I also found g=mg. I'm having trouble...

Hello, I feel a little out of place here, as I have no physics background whatsoever, but I was hoping you folks here might be able to help settle a debate. My brother and I like to have "what if" discussions, and one we had quite awhile ago was whether a person could walk across a swimming...

Homework Statement To build a triangular pile consisting of 120 balls, the number of balls in the base would have to be?? Multiple Choice a. 24 b. 30 c. 36 d. 45 Homework Equations The Attempt at a Solution The answer is 36. How do I get this answer and is...

Hi everybody. I keep on reading Rohatgi's book "An introduction to Probability and Statistics". Just now I am working in the following problem: We have n cells numbered 1 to n and n balls numbered 1 to n. We place at random the n balls in the n cells, with no cell receiving more than one ball...

1. A person drops a ball from the top of a building; 1 second later, a second ball is thrown straight up from the bottom of the same building. The ball that is thrown upwards has just the necessary speed to just make it to the top of the building. As the balls pass each other, they have the...

Homework Statement Determine all possible ways to placing three balls into three boxes, where there may be more than one ball in anyone of the three boxes. Could you determine all possible ways of placing 20 balls in 365 boxes? Homework Equations The Attempt at a Solution I know this problem...

Hi all, I’m trying to distribute M balls into N boxes. Each box has two compartments (thus 2N compartments total), each of which can hold one ball. There are more compartments total than balls. What I would like to do is calculate the number of boxes, on average: 1) With no balls (2...

Homework Statement In how many ways can 3 balls of different colours be put in 4 glass cylinders of equal width such that any glass cylinder may have either 0,1,2 or 3 balls? The Attempt at a Solution Using the formula for no. of ways for distribution of n distinct things into r...

Homework Statement At time t1, the boy throws a ball at an angle theta1 After some time (say t2), the boy throws another ball at an angle theta2 The initial velocity for both balls is the same (say v0) The balls collide at B, a distance of y (as shown in the attachment) the veritcal...

A 253.5 kg cannon rests on a frozen pond. The cannon is loaded with a 6.8 kg cannon ball and is fired horizontally. If the cannon recoils to the right with a velocity of 6.9 m/sec , then what is the velocity (in m/s) of the cannonball just after it leaves the cannon? Also would like a hint...

Homework Statement If n balls are distributed into k urns, what is the probability that the last urn contains j balls? Homework Equations The Attempt at a Solution not really sure how to do it. This is only a review question, not HW, but with that being known, I would...

[PLAIN]http://img178.imageshack.us/img178/4781/345b.jpg So I said v=v0-gt, and at the highest point, v=0, so t=v0/g. I also said uy=u0sinx-gt, and ux=u0cosx. So at t=v0/g, both balls have to be at their highest pint, and when uy=0, t=u0sinx/g...so equating the two times, I find...

Homework Statement 2 small spheres of charge "q" suspended from strings of length "l" are connected at a common point. one sphere has mass m, the other 2m. Assume angles theta_1 and theta_2 that strings make with vertical are small. (a) how are theta_1 and theta_2 related? (b) show that the...

Are open balls and neighborhoods the exact same thing? If not, could you please shed some light on this for me?

Let's consider a simple case with 2 balls and 3 boxes. Assuming all balls are the same and empty box is allowed. In addition, each box can take any number of ball. How many ways are there to place the balls into the boxes? Here is my way to solve the problem. For the first ball, there are 3...

Homework Statement Ball A is dropped from the top of a building of height h at the same time that Ball B is thrown vertically upward from the ground. When the balls collide, they are moving in opposite directions, and the speed of A is twice the speed of B. At what height does the collision...

Hi, I'm trying to design a solution to the problem of finding golf balls in the rough. I've had a few thoughts so far: - Image processing to detect white objects in a predominantly green environment - UV light emitter and detector to take advantage of fluoresence of the whitening coating of...

Homework Statement There are 50 balls in a bag, all are the same except for the color. 4 of them are white while the rest (46) of them are red. Now randomly draw balls from the bag, one at a time, without replacement. What is the expected number of red balls that you will draw before you...

Two balls are moving through space in the same direction, the balls have differiential masses and velocitys. Ball A is behind Ball B but is also moving faster so will soon collide with it, my question is "How fast will both balls be moving after they have collided?" Ball A: mass=10...

Homework Statement In space in the absence of gravity, there is a post of "infinite mass," meaning that the post is fixed or "nailed down" and cannot move. A ball of mass m1 is connected to the post by a cable of negligible mass of length L1. A second ball of mass m2 is connected to the first...

Two objects of different mass should fall at the same time, both with acceleration g. That is if the objects are in a vacuum, have the same initial speed and height. However, considering air resistance, the acceleration diminishes until both the drag and the weight are equal. Now, a canon ball...

Hi-- I'm doing an end of year project on the physics of trampolines. Anyone who has ever trampolined before knows that you can "double bounce" a person, such that one person bounces right before the other, thus launching the second bouncer higher into the air. In order to do a physics experiment...

Two balls of equal mass m undergo a collision. One ball is initially stationary. After the collision, the velocities of the balls make angles of 33° and 43° relative to the original direction of motion of the moving ball. If initial speed of moving ball is 5.4 m/s find the final speed. What...

Homework Statement There is total of 300 balls in the basket, 30 of them is red (rest is white). If we picked up, randomly, 4 balls, what is the probabilty that all of them is red ? 2. The attempt at a solution For one picked ball, probability that it's red is 30/300 = 1/10. If...

If a cylinder is rolling without slipping, C is the centre of zero velocity for a moment and O is the centre Does the angular rotation about O equal to the angular rotation about C, or is there only one angular rotation when a cylinder is rolling, that is the rotation about the point of...

I am working on a hobby project. I need 2 perfectly spherical, perfectly balanced, pure metal (ie. pure titanium, aluminum, etc.) balls made, and then I need one (the larger one) to be precisely drilled through the center. It is essential that everything is done in an extremely accurate manner...

Homework Statement A pendulum of mass m_1 is released at an angle theta_1 and strikes the pendulum of mass m_2, which rises to angle theta_2. The coefficient of restitution e for the two masses is given. Derive an expression for the angle theta_2. Homework Equations KE_1+PE_1=KE_2+PE_2...

Homework Statement near the surface of the Earth there is an electric field of about 150 V/m which points downward. 2 identical balls with mass 0.540 kg are dropped from a height of 2.0 m, but one of the balls is positively charged with q1 = +650 uC and q2 = -650 uC. use conservation of...

Homework Statement A Bag contains 4 balls.two balls are drawn at random,and are found to be white.what is the probability that all balls are white? Homework Equations P(B/A) = P(A intersection B) / P (A) The Attempt at a Solution A = Two balls are white. B = All four balls are...

Homework Statement Two billiard balls, one heading north at 15.0 m/s and a second heading south at 10.0 m/s, collide head-on. Take the collision to be perfectly elastic and choose the positive direction north. What is the post-impact speed of the first ball Answer: m/s What is...

Homework Statement Consider an elastic collision (ignoring friction and rotational motion). A queue ball initially moving at 2.6 m/s strikes a stationary eight ball of the same size and mass. After the collision, the queue ball’s final speed is 1.2 m/s. Find the queue ball’s angle (theta)...

Homework Statement There's a rod, 1 m long and by itself weighing 1 kg, with two balls attached at each of the sides, one weighing 2 kg, and the other 4 kg. The balls are put upon two scales. What force is applied upon each of the scales (e.g. what do the scales show)? Homework Equations...

The questions is pretty short... The source was a chat session and hence the simple sentence. I am stuck with this and thought that Homework Help doesn't attend out of the way questions and so I'm asking them here.