Balls Definition and 541 Threads

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? 2. Relevent equations At school, I'm currently learning Bayes' theorem, probability disribution and Bernoulli trials. The Attempt at a...

I'm trying to work out the following problem: Find the first two terms of the power series expansion for the volume of a ball of radius r centered at p in a Riemannian Manifold, M with dimension n. We are given that Vol(B_r(p)) = \int_S \int_0^r \det(d(exp_p)_{tv})t^{n-1}\mathrm{d}t...

Homework Statement From a bag containing 4 white and 6 black balls, 2 balls are drawn at random. If the balls are drawn one after the other, without replacement, find the probability that The first ball is white and the second ball is black Homework Equations The Attempt at a...

Homework Statement Suppose x,y \in X which is a normed linear space and x\neq y . Prove that \exists r>0 such that B(x,r) \cap B(y,r)=∅ Homework Equations Epsilon Ball B(x,r)={z \in X:||x-z||<r} The Attempt at a Solution So my attempt here is via contradiction and its not...

Homework Statement A 0.155-kg ball, moving in the positive direction at 13 m/s, is acted on by the impulse shown in the graph below. What is the ball's speed at 4.0 s? The graph is attached below. Homework Equations J = F Δt The Attempt at a Solution I thought that it might...

What is the significance of gravity on the torque of balls rolling down an incline? I know that gravity is able to exert a force, or torque by acting on the center of mass, causing an object to rotate. But what about rolling motion? Where would the axis of rotation be for a ball rolling down...

One ball is thrown upwards at 10 m/s, the other is thrown straight down (not dropped) also at 10 m/s. Which ball arrives first? This is more of a theoretical question than anything. I know the relevant equations such as v^2=u^2 +2as, but I was thinking that the height of the building has to...

[FONT=Lucida Grande]HELP PLEASE! My friend is suffering huge depression and stress and she really needs to hand in this assignment or she will fail... please if you can answer any of these questions! [FONT=Lucida Grande]A bag contains x pink balls and y yellow balls. Three balls are randomly...

Homework Statement A small ball of mass m is aligned above a larger ball of mass M = 0.63kg (with a slight separation), and the two are dropped simultaneously from height h = 1.8m. (Assume the radius of each ball is negligible relative to h.) a. If the larger ball rebounds elastically from...

Hi, I'm having a bit of trouble with the below practice problem from my textbook. The answer given in the back is -9.52 m/s, but there is no explanation. Thanks for any help. Homework Statement Two balls are thrown off of a 7.25 m high building both at an initial speed of 63.5 mph. However...

Homework Statement The entire problem is in the attachment.Homework Equations F = k*(|q||q0|)/(r^2) The Attempt at a Solution F = 8.99e9(.450uC*.450uC)/(3cm^2) = 6.068e8 This problem has me completely lost and I am turning to you guys as my last resort. I solved for F and have no idea what to...

Homework Statement Small masses m1 (m1 = 30 kg) and m2 (m2A = 5 kg; m2B = 10 kg; m2C = 40 kg; m2D = 50 kg; m2E = 30 kg) are each attached to a string of length 2.0 m. The other end of each string is attached to a common point on the ceiling. The masses are raised until each string is at an...

Homework Statement http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_41.pdf number 6III...

There are 5 players and me. If I throw numerous balls in the air and the chances of each individual player catching a ball is as follows: player 1: 13% player 2: 16% player 3: 14% player 4: 15% player 5: 18% Please show working: 1) What is the chance that at least one player catches a...

Hey Everybody, I am supposed to model the trajectory of a golf ball. I have been given the equations for velocity as a function of its derivative with respect to time. I am supposed to find the x-range as a function of the angle θ. (Pardon my bad latex skills, I will fix mistakes)...

Homework Statement Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Initially ball A is moving along the y axis at +2.0 m/s, and ball B is moving to the right along the x axis with speed +3.7 m/s. After the collision (assumed elastic)...

Bob has two balls. He releases one ball from a platform of height H. Just as that ball strikes the ground he releases the next ball from the same height H. Assuming that the first ball bounces perfectly, (i.e. reversing only the direction of its velocity when it strikes the ground), at what...

A box contains V balls of which N_{g} are green, N_{r} are red and V-N_{g}-N_{r}=N_{b} are blue. Now somebody shakes the box vigorously, brings it to rest and then observes the arrangement of the balls in the box. Suppose this is repeated many times so that probabilities of different ball...

Homework Statement Two balls are juggled so that each ball is in the air for 2.000s, and the second ball is thrown UP at the instant the first starts down. Find the height above the throwing hand where the two balls pass. (Assume gEARTH = 9.800m/s2 down) TT=2.000s g=9.800m/s2 down...

Consider two balls on an inclined track with a constant angle. Ball Q is released from rest a tthe top of the track. Ball P is given an initial velocity directed up the track. Both balls have a constant acceleration directed down the track. at the instant that the balls collide, ball Q is going...

Six balls are thrown from the top of a building. Two balls are dropped from rest, two are thrown downward with a velocity of 10 m/s and two are thrown upward with a velocity of 10 m/s. Each ball has a differing mass as well, such as the two balls thrown from rest, one has a smaller mass than the...

Homework Statement One charged plastic ball is vertically above another in a test tube as shown. The balls are in equilibrium a distance "d" apart. If the mass of the upper ball is reduced by a factor of four, the distance between the balls in the test tube would become : 1) 4d 2) 8d 3)...

Homework Statement I dropped a ball from different heights, and got height they bounced up to, but I need a formula for it. Data Gravity = 9.800 m/s2 [Initial Height(cm)]----------[Bounced Height(cm)] 100.0---------------------------81.00 90.00---------------------------75.00...

Homework Statement Ball A is dropped at t=0 from a window. At t=6, the ball hits the ground. Neglect air resistance for question a) Suppose that at t=1, Balls B and C are thrown vertically down from the same window. Ball C has a greater initial velocity than Ball B, as shown by their...

Homework Statement A blue ball is thrown upward with an initial speed of 20.4 m/s, from a height of 0.5 meters above the ground. 2.5 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 9.8 m/s from a height of 23.9 meters above the ground. The force of...

One ball is selected from 100 at a time, without replacement. Of these balls, r of them are red. What is the probability that the first ball picked will be red? The 50th? The last? Solution: I don't understand why it matters which pick it is. I know that "without replacement"...

1. Homework Statement [/b] Two smooth uniform spheres, A and B, are of the same size, but A has twice the mass of B. They are placed at rest on a smooth horizontal table and A is projected directly towards B with speed U. The spheres collide, and then B strikes a barrier perpendicular to its...

Homework Statement Let \displaystyle f:{{\mathbb{R}}^{n}}\to \mathbb{R} a continuous function. Proove that: If \displaystyle f\left( p \right)>0 then there's a ball \displaystyle {{B}_{p}} centered at p such that \displaystyle \forall x\in {{B}_{p}} we have \displaystyle f\left( x...

Homework Statement (It includes a diagram so I'm just going to link it) #22 from Chapter 7 of the People's Physics Book (second to last page, with the table) http://scipp.ucsc.edu/outreach/07Momentum.pdf Homework Equations p(i)=p(f) p(f)x=m*v*cosin(theta) [I "made these up", so to speak, but...

Hi guys, really simple question but... http://img341.imageshack.us/img341/5447/ballsra.jpg I'm not quite sure on how they ended up with the expression for P(exactly one match). I would have done it in a more straight forward way, simply define A: matching the colour red in the red box only. B...

Homework Statement Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9 white and 4 blue identical balls. What is the probability that they are one red, one white and one blue? Homework Equations The Attempt at a Solution The question...

The jar has a radius of 6" and a height of 24" and each ball has a radius of 1". So I found the volume of the jar which is \pi6^{2}(24) = \approx 2,714.33605 and the volume of the balls which is \frac{4}{3}\pi1^{3} = \approx 4.1887902 And then I divided how many of the balls can go into the...

Homework Statement A ball of mass m = 1.9 kg moving with a speed of v0 = 20.1 m/s strikes an identical ball which was initially at rest. After the collision, the incoming ball (ball 1) goes off at q1 = 26° relative to its original direction and the struck ball (ball 2) moves off at q2 = 36° as...

Homework Statement Question: A 12kg ball traveling at 5 m/s strikes a stationary ball of 7kg. After the collision the balls are 60 degrees apart, each 30 degrees either side of the original path of the striking ball. Calculate the speed of both balls after collision?Homework Equations...

Homework Statement A tennis ball of mass m_t is held just above a basketball of mass m_b. With their centers vertically aligned, both are released from rest at the same moment, so that the bottom of the basketball falls freely through a height h and strikes the floor. Assume an elastic...

Homework Statement Two elastic balls of mass m1 = 0.3kg and m2 = 0.2kg are hanging on a thin rope so that their centre of gravity is on the same height. ball 1 goes out of balance raising it up to h0 = 0.05m Then letting it go hitting ball 2. Calculate the maximum height of both balls reaching...

Homework Statement Homework Equations I=mr^{2} L=ωI ω=\frac{L}{I} The Attempt at a Solution I thought that since the moment of inertia was larger for the ball on the outside its angular speed would be slower. So then it would take longer to hit the wall.

1. A ball is dropped from a height of 79 m. Simultaneously a ball is thrown upward from the ground at a velocity of 28 m/s. How much time passes until the balls are at the same height. I'm not really sure what equation to use or how to approach.

Could someone please show that an open ball is open where the definition of "open" is: A set is open if for each x in U there is an open rectangle A such that x in A is contained in U. Where an open rectangle is (a_1,b_1)×…×(a_n,b_n). I also realize that one can use rectangles or balls, but I...

I'd like to simulate the interaction between these magnetic balls on my computer. I suppose they are magnetic dipoles, how would I go about finding out the forces applying between 2 of them in a specific configuration ? Do I need to find the magnetic field and then apply the Lorentz force...

two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster? i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine...

Suppose you have 3 balls, all of equal mass, M. They are connected to each other by equal-length (each length L) strings of negligible mass, such that one ball is suspended in the middle and the two balls at the end are themselves suspended from the ceiling at two points, a distance X from one...

Homework Statement This figure shows two identical billiard balls before and after a glancing collision. Determine the speed of the other ball. Homework Equations 0=mv1sin30- mv2sin60 The Attempt at a Solution v1= [(0.05m/s)sin60]/(sin(30))= 0.087 m/s Here I am...

Homework Statement A ball of mass 4.5 kg is moving 16 m/s east when it collides with a stationary 6.2kg ball, which moves at a velocity 10 m/s after the collision. Was this an elastic or inelastic collision? Explain your choice. Va = 16 m/s Ma = 4.5 kg Mb = 6.2 kg Vb' = 10 m/s...

Homework Statement Two billiard balls of equal mass undergo a perfectly elastic head on collision. If one ball's initial speed was 2.00 m/s, and the other's was 3.00 m/s in the opposite direction, what will their speeds be after the collision? Va = 2 m/s Vb = 3 m/s Homework...

Conditional probability & "r balls randomly distributed in n cells" Homework Statement I'm posting this in hope that someone can give me a correct interpretation of the following problem (problem V.8 of Feller's Introduction to probability theory and its applications VOL I): 8. Seven balls...

Homework Statement A 5.0-kg object has a velocity of 6.0 m/s, east when it explodes into two 2.5-kg objects. After the explosion one of the objects has a velocity of 4.0 m/s at an angle of 50° north of east. What is the magnitude and direction of the velocity of the other object after...

[SIZE="4"][SIZE="3"]A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.14 later. You may ignore air resistance.A- If the height of the building is 19.3 , what must the initial speed be of the first ball if both are to hit the...

I typed the question and my attempt at a solution below... It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.

If 2 similar pith balls of mass m are hung from a common point with the help of 2 long silk threads. The balls carry similar charges q. Assuming theta is very small find an expression for x. Also assuming that each ball loses charge at a rate of 1*10^-9 c/s at what instantaneous relative speed...