1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Related Rates Problem

  1. Jun 30, 2008 #1
    1. The problem statement, all variables and given/known data
    A rocket is launched vertically and is tracked by a radar station located on the ground 5 mi from the launch pad. Suppose that the elevation angle θ of the line of sight to the rocket is increasing at 3° per second when θ=60°. What is the velocity of the rocket at this instant?

    2. Relevant equations

    3. The attempt at a solution
    0=c(dc/dt) - y(dy/dt)



    tan π/3=y/5
    5tan π/3=y

    c2=square root of 34

    Can I just plug in 3 for y, square root of 34 for c, and π/60 for dc/dt
  2. jcsd
  3. Jun 30, 2008 #2


    User Avatar
    Homework Helper

    This would be OK up to here,

    But this is not the rate of change of c, but the rate of change of [tex]\theta[/tex].

    For your definitions, x = 5 and y is the altitude of the rocket. So you are looking for dy/dt (since the rocket is going straight up) and you will need to differentiate

    [tex]tan\theta = \frac{y}{x}[/tex] .

    (The rate at which the hypotenuse, c, is changing is not needed in this problem.)
  4. Jul 2, 2008 #3
    I realized my mistakes. I now have sec2θ dθ/dt = (dy/dt)/5.
    Should I plug in dθ/dt in degrees or radians?
  5. Jul 2, 2008 #4


    User Avatar
    Homework Helper

    In mathematical expressions, angles are expressed in radians.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Related Rates Problem Date
Related Rates problem Dec 11, 2017
Need a little help with this related rates problem Jul 12, 2016
Related rates problem help May 11, 2016
Calculus - Related Rates Problem Mar 11, 2016
Related Rates Sand Pile Problem Jan 11, 2016