My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 7th, 2013, 09:45 AM   #1
Newbie
 
Joined: Dec 2012

Posts: 10
Thanks: 0

a problem on a moving searchlight beam; implicit diff.

PROBLEM

Moving searchlight beam The figure shows a boat 1 km offshore, sweeping the shore with a searchlight. The light turns at a constant rate,

a. How fast is the light moving along the shore when it reaches point A?
b. How many revolutions per minute is 0.6 rad/sec?

(There is a figure provided. It shows a right triangle with it's hypothenuse facing the left with points BCA reading clockwise. Point B represents the location of the boat. Point C and A are along the shore. There is an angle attributed to point B. The hypothenuse represents the searchlight. Line BA equals 1 km.)

ATTEMPT

So, we are tasked to find , which represents the speed of the searchlight moving along the shore. Part A asks us to find the speed "when it reaches point A", but the speed should be consistent throughout because is consistent (?).

I look for a relation to describe and felt that was sufficient. When differentiated, we arrive with the form:





Rearrangement to solve for ,



Now, the problem is that I do not know the value for and , and when I seek to evaluate these variables; it turns out that the triangle cannot be fully described with just an angle and a side.

Is there something I'm overlooking?
Lambin is offline  
 
March 7th, 2013, 10:11 AM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: a problem on a moving searchlight beam; implicit diff.

You may find these topics helpful:

http://www.mymathforum.com/viewtopic...thouse#p129431

http://www.mathhelpboards.com/f52/ka...ed-rates-3395/

You asked if the speed of the beam along the shore should be constant...can you see that this would only be true if the shoreline was circular, and the beam was located at the center of the circle?
MarkFL is offline  
March 7th, 2013, 02:14 PM   #3
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: a problem on a moving searchlight beam; implicit diff.

Hello, "Lambin!

Your work is correct, but some of it is unnecessary.


Quote:
Moving searchlight beam
The figure shows a boat 1 km offshore, sweeping the shore with a searchlight.
The light turns at a constant rate,

a. How fast is the light moving along the shore when it reaches point A?

Code:
                            * B
                         * @|
                      *     |
                  *         | 1
              *             |
          *                 |
    C * - - - - - - - - - - * A
                 x






\sec^{^2}0)(-0.6) \:=\:-0.6\text{ km/sec}" />




Quote:
b. How many revolutions per minute is 0.6 rad/sec?



soroban is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
beam, diff, implicit, moving, problem, searchlight



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
how to solve this problem of car moving?? gen_shao Algebra 8 January 8th, 2014 12:47 PM
relative rate of moving problem asifrahman1988 Calculus 1 March 17th, 2013 03:24 AM
Final Implicit Diff Word Problem I will ask help for mathkid Calculus 3 November 13th, 2012 12:40 AM
Ladder sliding down wall problem (Implicit Diff) mathkid Calculus 17 November 12th, 2012 07:59 PM
Implicit Diff. Problem David_Lete Calculus 0 November 1st, 2009 09:11 AM





Copyright © 2019 My Math Forum. All rights reserved.