2. (a) State Fermat's principle for the propagation of a light ray from point P at (x1,y1)to Q at (x2, y2), expressing the principle as a problem in Calculus of Variations.(b) Suppose c(y) is the speed of light in a medium, given byc(y)Ywhere a is a constant. Find the path of a light ray between the points P: (−1,3)and Q (1, 3). Is there more than one possible path?(c) Sketch the path of the light ray, and interpret what an observer at Q would see ifthere were a light source at P.

Step 1: Solution to Problem 2 (a) Fermat's Principle and Variational FormulationFermat's…

Answered: 2. (a) State Fermat's principle for the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
1. A particle moves along the x-axis so that its velocity at any given time is = 2t - 3 and x (0) = 3. v(t) = a.) Find the equation for position of the particle as a function of t, x(t). b.) Find the position of the particle at t = 3. c.) At what values of t does the particle change direction? d.) Where is the particle when the position is a minimum?
In physical chemistry, it is shown that the pressure P of a gas is related to the volume and temperature through the van der Waals equation: (P +) cv (V – b) = nRT Where a, b, n and R are constants. The critical temperature Tc of a gas is the highest temperature at which the liquid and gas phases can exist as separate phases. a) When T = Tc. the pressure P is given as a function only of the volume P(V) The critical volume Vc is the volume for which P'(V) = 0: and P"(Vc) = 0. Find Vc b) Find the critical pressure Pc = P(Vc) and there by express Tc in terms of a, b, n and R.
A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128/257 feet. The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second.The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)
Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right where the origin is set to be a certain point in space. At what point on that path should the engine be turned off in order to coast along the tangent line to another ship that is not moving relative to the origin of the path and is at the point (10, 3)? (Once the engine is turned off, there is no force pushing it in a certain direction, so it continues along the same path that the velocity is pointing at that specific time. This means it continues along a path that is a tangent line to the original curve.) Note: The graph really helps on this one. Go ahead and draw it and you will see that it helps. It's all about the picture on this one! Coordinates:
The path of flight (trajectory) of a football thrown by a quarterback is described by the +0) ². x² following function: y(x) = - where y = vertical position of football relative to the ground Linear model yo = vertical launch position of football relative to the ground horizontal position of football relative to launch position g=magnitude of gravitational acceleration vo = launch speed = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory? Nonlinear model g 2v² cos² e Exponential model + (tan)x + yo Trigonometric model
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?

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