March 19th, 2017, 05:22 PM  #1 
Member Joined: Feb 2017 From: East U.S. Posts: 33 Thanks: 0  Related Rates
A patrol car is parked 30 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes angles of θ = 45°, θ = 60°, and θ = 80° with the line perpendicular from the light to the wall? (Round your answers to two decimal places.) Things I know: 1) tan(θ) = x/30 OR 1/30(x) 2) d(θ)/dt = 60pi 3) I need dx/dt I also know there's something to do with sec^2(θ) and/or cos((45/60/80))^2 I just wanna learn this for myself, it's not for a class. It's super frustrating. Please help... Thanks! 
March 19th, 2017, 05:35 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239 
$30 \, rev/min \, = 60\pi \, rad/min$ $\tan{\theta} = \dfrac{x}{30}$ $\sec^2{\theta} \cdot \dfrac{d\theta}{dt} = \dfrac{1}{30} \cdot \dfrac{dx}{dt}$ $\dfrac{30}{\cos^2{\theta}} \cdot \dfrac{d\theta}{dt} = \dfrac{dx}{dt}$ sub in $60\pi \, rad/min$ for $\dfrac{d\theta}{dt}$ and the desired value(s) of $\theta$ into $\cos^2{\theta}$ to calculate $\dfrac{dx}{dt}$. note $\dfrac{dx}{dt}$ will be in units of ft/min 
March 23rd, 2017, 11:56 AM  #3  
Member Joined: Feb 2017 From: East U.S. Posts: 33 Thanks: 0  Quote:
 
March 25th, 2017, 05:15 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239  
March 25th, 2017, 06:00 PM  #5 
Member Joined: Feb 2017 From: East U.S. Posts: 33 Thanks: 0  Never mind that. So I plugged in everything you said and got "20491.38" but that's not the right answer according to this website I'm using. This is exactly what I put into my calculator 30/cos(45)^2 which gives me "108.71015", then I multiply all of that by 60pi to get "20491.38" (rounded to two decimal places.) What am I doing wrong? 
March 25th, 2017, 07:28 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239 
If you input degrees, you calculator should be in degree mode ... $\dfrac{30}{\cos^2(45^\circ)} = 60$ 
March 25th, 2017, 10:32 PM  #7 
Member Joined: Feb 2017 From: East U.S. Posts: 33 Thanks: 0  Ok, so in that case, I got "11309.73(rounded)" as my answer and it's still not working..... Could you please just tell me what the answer should be? I'm sorry to annoy you on the forums, but I've been trying to figure this out for 3 whole days and it's driving me crazy.....

March 25th, 2017, 10:53 PM  #8 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,105 Thanks: 368 Math Focus: Yet to find out. 
It's likely your calculator isn't set to degrees, as skeeter said. What is the model of your calculator?

March 26th, 2017, 12:33 AM  #9  
Member Joined: Feb 2017 From: East U.S. Posts: 33 Thanks: 0  Quote:
I'm trying to find dx/dt using this formula: $\dfrac{30}{\cos^2{\theta}} \cdot \dfrac{d\theta}{dt} = \dfrac{dx}{dt}$ So I plug everything in and it's not right... It should be 60*60pi, right?  
March 26th, 2017, 12:42 AM  #10  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,105 Thanks: 368 Math Focus: Yet to find out.  Quote:
Note that $45^{\circ} \cdot \dfrac{2 \pi}{360^{\circ}} = \dfrac{\pi}{4} \ radians$. Last edited by Joppy; March 26th, 2017 at 12:48 AM. Reason: lost pi  

Tags 
rates, related 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Related Rates Help  Mathman97  Calculus  4  October 25th, 2014 08:04 PM 
Related Rates  rileybreann13  Calculus  1  May 26th, 2013 05:02 PM 
Related Rates  chocochippyx2  Calculus  3  March 24th, 2011 03:00 PM 
related rates  mathman2  Calculus  3  February 12th, 2009 06:52 AM 
Related Rates Help Please  pranavpuck  Calculus  11  November 30th, 2008 10:32 AM 