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!

Moving point and it's distance relative to a fixed point

  1. Aug 26, 2016 #1
    Not sure whether this is an intro physics or intro calculus/related rates problem.

    1. The problem statement, all variables and given/known data

    Suppose a point P lies at (x,y)=(0,1) meters.

    A car is travelling at 30 meters/second along the x-axis towards +∞.

    Define r to be the distance between P and the car at any time t.

    I need to know the rate of change of the distance between P and the car with respect to time (dr/dt) ?

    2. Relevant equations
    Pythagorean theorem....I attached a picture

    Attached my attempted solution....tried 2 methods. I do not know what θ(t) or dθ/dt is so that's why I havent been able to get it.

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Aug 26, 2016 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Forget the angle. Just think of r as a function of x. (You know what dx/dt is.)
  4. Aug 26, 2016 #3
    Thanks. I got it now. Sometimes I just get one track minded and forget to think about other ways of looking at it.
    v = the velocity
    x = horizontal component of r

    $$ r^2 = x^2+1^2 $$
    $$ r = \sqrt(x^2 +1) $$
    $$\frac {dr} {dt} =\frac {1} {2} \frac {1} {\sqrt(x^2 +1)}\frac {d} {dt} (x^2 +1) $$
    $$ =\frac {1} {2} \frac {1} {\sqrt(x^2 +1)} 2x \frac {dx} {dt} $$
    $$ =\frac {xv} {\sqrt(x^2 +1)} $$

    Since $$ x(t)=x_0+vt$$
    we have $$\frac {dr} {dt} = \frac {v(x_0+vt)} {\sqrt((x_0+vt)^2 +1)} $$

    and also $$r(t) = \sqrt(x^2 +1)= \sqrt((x_0+vt)^2+1)$$
    Last edited: Aug 26, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Moving point and it's distance relative to a fixed point
  1. Fixed points (Replies: 2)

  2. Fixed point iteration (Replies: 2)

  3. Finding a Fixed Point (Replies: 2)

  4. Fixed point theorem (Replies: 4)