1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Applied maths urgent

  1. Mar 14, 2015 #1
    Problem 1 20 marks (i) ˆx = (1, 0) and ˆy = (0, 1) are the Cartesian unit vectors and the vectors v1 and v2 are defined as v1 = −4ˆx + 0ˆy , v2 = 2ˆx − 7ˆy . Determine the polar coordinate unit vectors ˆr and ˆθ for v1 and v2 and hence express v1 and v2 as a linear combination of ˆr and ˆθ. [4]

    (ii) A particle’s motion is described by the following position vector r(t) = αtxˆ + (βt2 − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]

    (iii) By differentiating with respect to time r(t), given in (ii) show that the velocity vector written in a Cartesian basis for this particle is v(t) = αxˆ + (2βt − 1)ˆy . [2] (iv) Using the ˆr and ˆθ you found in (ii) above, write v(t) as a linear combination of rˆ and ˆθ. [4]

    (v) Differentiate the expression for r(t) you got in part (ii) (in terms of ˆr and ˆθ, and using the expressions ˙rˆ = ˙θ ˆθ , ˙ˆθ = − ˙θrˆ derived in the lectures, show that you obtain the same answer as in part (iv) [6]

    where r(vector) = r modulus * r
    r^ = cos(pheta)x + sin(pheta)y
    pheta^ = -sin(pheta)x +cos(pheta)y

    i am able to do i) and ii) but unbale to expres v(t) in terms of r and pheta
  2. jcsd
  3. Mar 14, 2015 #2


    User Avatar
    Homework Helper

    What did you get for the position vector?
    What do you get when you take the time derivative of that expression?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted