Question Solved1 Answer 3. Often times in football a punter may not need to kick the ball very far, but rather kick the ball high so that the other players have a lot of time to run down and make a tackle. If a punter punts a ball from 1.5 m high with an initial velocity of 25 m/s at an angle of 72º to the horizontal, what are the maximum height and time of flight for the ball? Assume the ball lands on the ground. [6 A]

One of the many interesting fundamental particles in nature is the muon ?. This particle acts very much like a heavy electron and has a mass of 106MeV/c2, compared to the electron's mass of just 0.511MeV/c2. (Here we are using E=mc2 to obtain the mass in units of energy and the speed of light c). Unlike the electron, the muon has a finite lifetime, after which it decays into an electron and two very light neutrinos ( ?). We'll ignore the neutrinos throughout this problem. If the muon is at rest the characteristic time that it takes to decay is about 2.2?s (??=2.2×10?6s). Most of the time though, particles such as muons are not at rest and, if moving relativistically, their lifetimes will be increased by time dilation. In this problem we will explore some of these relativistic effects. Let's begin by looking at some muons moving at various speeds relative to a stationary observer. Part A If a muon is traveling at 70% the speed of light, how long will it take to decay in the observer's rest frame (i.e., what is the observed lifetime)? Express your answer in microseconds to two significant figures. View Available Hint(s) ?? = ?s SubmitPrevious Answers Incorrect; Try Again; 4 attempts remaining Part B If a muon is traveling at 99.9% the speed of light, how long will it take to decay in the observer's rest frame? Express your answer in microseconds to two significant figures. ?? = 49•10?649{\cdot}10^{-6} ?s SubmitPrevious AnswersRequest Answer Incorrect; Try Again; 5 attempts remaining Part C What is the total energy E of a muon traveling at 99.9% the speed of light? Recall that the rest energy of the muon is approximately 106MeV. Note that 1GeV=1000MeV. Express your answer in billions of electron volts to three significant figures. View Available Hint(s) E = GeV Submit Cosmic rays are constantly raining down on the earth from outer space. (Figure 1)The majority of these cosmic rays are protons, and when they crash into the upper atmosphere, they can convert into particles called pions ( ?), which subsequently decay into muons with a characteristic lifetime of ??=2.6×10?8s (in their rest frame). These muons can then continue down toward the earth until they too decay (into electrons, which are so light that they stop very quickly in the atmosphere). Let's look at how time dilation affects these cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the pion has a velocity of 99.99% the speed of light and decays into a muon, which, owing to kinematics, has a downward velocity of 99.9943% the speed of light. Part D How far would the pion travel before it decayed, if there were no time dilation? Express your answer in meters to two significant figures. d? = m SubmitRequest Answer Part E How far would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. d? = m SubmitRequest Answer Part F Now, let's consider the effects of time dilation. How far would the pion actually travel before decaying? Express your answer in meters to three significant figures. d? = m SubmitRequest Answer Part G How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. d? = km SubmitRequest Answer Provide Feedback

Identify each variable as quantitative or qualitative.a) ethnic origin of a candidate for public officeb) score (0-100) on a placement examinationc) fast-food establishment preferred by a student(McDonald's, Burger King, or Carl's Jr.)d) mercury concentration in a sample of tuna

•• An infinite slab of charge of thickness 2zo lies in the xy-plane between z = -zo and 46. z = +z0. The volume charge density p (C/m³) is a constant. a. Use Gauss's law to find an expression for the electric field strength inside the slab (-zo zo). c. Draw a graph of E from z = 0 to z = 3z0.

Exercise 5 : Two particles in a potential well Consider two noninteracting particles, both of mass m, in a quadratic potential well (i.e. har- monic oscillator potential). For the case with one particle in the single-particle state [n) and the other in state k) (n + k), calculate the expectation value of the squared interparticle spacing ((21 – 222) assuming: 5.1 The particles are distinguishable 5.2 The particles are identical spin-o bosons 5.3 The particles are identical spin-1/2 fermions in a spin triplet state. Hint: use bra-ket notation as much as possible. Remember that for the harmonic oscillator it is easiest to use, whenever possible, raising and lowering operators to evaluate expectation values (i.e. to evaluate integrals).

Problem 4 A new test is developed for cancer detection with sensitivity 0.80 and specificity 0.91. Assume this cancer affects 6% of the population. (a) Sketch the probability tree for this test and label each branch appropriately. (b) Calculate the Bayes probability that an individual has cancer if their test result is posi- tive. (c) Calculate the Bayes probability that an individual does not have cancer if their test result is negative. (d) Compute a naive Bayes estimate for either b or c. Your choice! Then, briefly explain why is this referred to as "naive".

Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What causes Bailey's beads to form? Part b = 10 pts 8. During an annular eclipse of the Sun, we see a bright annulus or "ring of fire." During a total solar eclipse we see the corona during totality. In both events, the Moon is directly in line with the Sun and Earth. What differentiates these two types of solar eclipses? That is what aspect of the eclipse geometry has changed to create an annular eclipse rather than a total eclipse? 115 pts