Verify the given velocity vector

Assignment Help Mathematics
Reference no: EM131005831

The unit polar basis {er, eθ} is related to the standard Cartesian basis {i. j} as follows:

er = cos θi + sin θj, eθ= - sin θi + cos θj

1. Verify that

der/dt = dθ/dt · ( -sin θi + cos θj) = (dθ/dt) eθ; (deθ/dt) = -dθ/dt · (cos θi + sin θj) = -(dθ/ dt) er

2. Relative to polar coordinates, the position vector of an object moving in the plane can be written as

r (t) = r(t)er.

Verify that the velocity vector is

v(t) = (dr/dt) er + r (dθ/dt)] eθ,

and then show that the acceleration vector is

a(t) = [(d2r/dt2) - r(dθ/dt)2]er + [r(d2θ/dt2) + 2(dr/dt) · (dθ/dt)] eθ.

Reference no: EM131005831

Questions Cloud

What is the annual inventory cost of the current system : What is the annual inventory cost of the current system in which product is produced, labeled, and packed in Malaysia before being shipped to the DC?
Variance of the number of days until the prisoner : Assuming that the prisoner will always select doors 1, 2, and 3 with probabilities 0.5, 0.3, 0.2, what is the expected number of days until he reaches freedom? Assuming that the prisoner is always equally likely to choose among those doors that he..
What is the composition of the two phases and the pressure : The laboratory division of your company has sent you the following data for the system n-pentane (1) propionaldehyde (2) at 35 °C: The activity coefficients of the two components at infinite dilution are 4.0 and the saturation pressures of the pur..
Independent of the arrival process : The service times of the arrivals are independent exponential random variables with rate μ, and are independent of the arrival process. Customers depart the system when their service ends. Let N be the number of arrivals before the ?rst departure.
Verify the given velocity vector : Relative to polar coordinates, the position vector of an object moving in the plane can be written as r (t) = r(t)er. Verify that the velocity vector is v(t) = (dr/dt) er + r (dθ/dt)] eθ.
What is bubble pressure of the mixture : Use the data below for the system benzene(1)/acetonitrile(2) at 45 °C to answer the following question: What is the saturation pressure of the pure components at 45 °C?
Transition probabilities of markov chains : (a) If F is the exponential distribution with rate λ, which, if any, of the processes {Xn}, {Yn} is a Markov chain? (b) If G is the exponential distribution with rate μ, which, if any, of the processes {Xn}, {Yn} is a Markov chain? (c) Give the trans..
Find total expected return : (a) Find your total expected return. (b) Find the value of t that maximizes the total expected return.
Calculate the conditional distribution : Find the conditional distribution of T given that N = n. Calculate the conditional distribution of N, given that T = t, and notice that it is distributed as 1 plus a Poisson random variable with mean λ(1 - p)t.

Reviews

Write a Review

 

Mathematics Questions & Answers

  What is the roller angular speed

a printing press has a roller 22 inches in diameter. A point on the roller's surface moves at a speed of 109 feet per second. What is the roller's angular speed?

  State a system of equations to model the problem

a) write a system of equations to model this problem b). graph this system and use the graph to estimate how much was invested in each fund?

  Find probability and data representation

If order of the draw were important in a lottery, what would be the effect on odds of winning, if any? Explain. Find Probability and data representation

  Consider the cubic equation

Consider the cubic equationax3 + bx2 + cx + d = 0, (1)where a, b, c, and d are real input coefficients. Develop a matlab program to find all roots of equation (1) using the appropriate methods. Your program can not use the matlab built-in functions f..

  Determine the p-value for the test

Identify the null hypothesis and the alternative hypothesis. Determine the P-value for the test. Show all work; writing the correct P-value, without supporting work, will receive no credit

  Find the three integers

sum of three integers is 194, the sum of the first and second integers exceeds the third by 76, the third integer is 61 less than the first. find the three integers.

  State a scale model of a museum made of cubic blocks

A scale model of a museum made of cubic blocks. In my answer document sketch the view as it would appear from 2nd avenue.

  Basic probability problems

Basic probability problems

  Surface area of the cylinder

Build a three dimensional shape and prepare a set of questions to be presented to the class for problem solving. Questions should encourage students to cover the concepts of perimeter, volume, surface area, number of vertices, faces, and edges ass..

  Explain traveling along linear paths

traveling along linear paths, and you need to find the coordinates at which they might potentially collide. Suppose the two lines are 2x + 3y = 8 and 4x - y = -2. Solving the system of equations would give you the (x, y) coordinates of the possibl..

  In which direction is the x-coordinate moving

A point is moving on the graph of [5x^3 + 6y^3 = xy]. When the point is at P= [ (1/11), (1/11) ] its y-coordinate is increasing at a speed of 5 units per second. What is the speed of the x-coordinate at that time and in which direction is the x-co..

  How many ads of each type should be used

Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd