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: Dynamics question (polar kinematics). Please help.

  1. Feb 2, 2009 #1
    A rocket is fired vertically and tracked by a radar station on the ground, a distance (r) away from the rocket. When the station reads an angle of (theta) = 60* between the rocket and the ground, we are given that the distance r = 30,000ft, r(double-dot) = 70 ft/sec, and theta(dot) = 0.02 rad/sec. Find the magnitude of the velocity and acceleration of the rocket at this position.

    I know that to solve this, you need to find r(dot), and that this is somehow related to r as a function of time. I do not understand how to get this relationship, or how to find r(dot). Can anyone please help?
  2. jcsd
  3. Feb 3, 2009 #2


    Differentiating with respect to time and using the chain rule gives




    Why? Differentiate this expression again to arrive at an expression for r double dot in terms of the unit vectors r and theta. This should get you started.
  4. Feb 3, 2009 #3
    Forgive my ignorance, but what does the "^" above r and theta mean, and what is the difference between the r with and without the ^?
  5. Feb 3, 2009 #4
    The ^ represents the unit vector. In Cartesian coordinates it's

    [tex]\hat{x}\mbox{ and }\hat{y}[/tex]

    The r without the hat (^) is the magnitude of r. Have you been exposed to polar coordinates and the associated unit vectors?
  6. Feb 3, 2009 #5
    Yes, I understand vectors, I just have seen it with different notations.

    I still do not understand what you are trying to say with the expressions in your first reply. I do not get how to relate time to the values of r and theta, if a specified time is not given.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook