1. Not finding help here? Sign up for a free 30min 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!

Derivative as a rate of change exercise

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data

    A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°?

    This is the diagram:
    https://scontent-a-lax.xx.fbcdn.net...=8c58e875096c8045213bef3bff034736&oe=54BD392F
    Where:
    • α is the angle the light beam makes with the siren (and it is a variable)
    • dα/dt is the angular velocity of the light beam (and it is a constant; 30 revolutions per minute)
    • x is the length of what the beam hits in the wall (it is a variable)
    • dx/dt is velocity on how much light is being struck in the wall (it is a variable, and what's we are supposed to compute with the given data)
    • Also we have the distance between the police car and the wall, which is also a constant and is 50 feet.
    Ok, before going to the formulas, according to my textbook the answers should be:
    • When the angle is 30° (= 0.524 rad) the velocity is 200π/3 feet per second
    • When the angle is 60° (= 1.047 rad) the velocity is 200π feet per second
    • When the angle is 70° (= 1.222 rad) the velocity is approximately 427.43π feet per second

    2. Relevant equations

    Well, this is a calculus problem, it does not take a pre-shaped formula as in physics or chemistry. However, we are dealing with derivatives as a rate of change. I found the relationship which may lead to the problem answer:

    If we consider the previous diagram the formulas are:
    • x=50tan(α) which leads to the one below
    • dx/dt=50(sec2α)(dα/dt)= 50(1/cos2α) (this is the equation I used for attempting to solve the problem)
    NOTE: For getting the second equation, I used the trigonometric derivatives rules

    3. The attempt at a solution

    I did use the last formula; replacing with the given data we get:

    For the angle of ,524 rad
    dx/dt=50(1/cos2(,524))=66.69 ft/s which is not the same as 200π/3 ft/s
    For the angle of 1,047 rad dx/dt=50(1/cos2(,524))=201.96 ft/s which is not the same as 200π ft/s
    For the angle of 1,222 rad dx/dt=50(1/cos2(,524))=423.4 ft/s which is not the same as 427.43 ft/s

    I need to see what I'm doing wrong; I've been stuck in this problem for about an hour and a half :(
     

    Attached Files:

  2. jcsd
  3. Oct 15, 2014 #2

    Mark44

    Staff: Mentor

    In your formula for dx/dt, it looks like you have lost dα/dt at the end.
     
  4. Oct 15, 2014 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In addition to Mark44's comments, don't change everything to decimals. Use ##30^\circ = \frac \pi 6##radians and ##30##rpm##=\pi##rad/sec.
     
  5. Oct 15, 2014 #4
    Thanks everyone, I checked and I got it right.
     
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: Derivative as a rate of change exercise
Loading...