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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
    Let

    [tex]\vec{r}=r(\theta{})\hat{r}[/tex]

    Differentiating with respect to time and using the chain rule gives

    [tex]\vec{\dot{r}}=\dot{r}\hat{r}+r\frac{d\hat{r}}{d\theta{}}\frac{d\theta{}}{dt}[/tex]

    and

    [tex]\frac{d\hat{r}}{d\theta{}}=\hat{\theta}[/tex]

    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.
     
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