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Calculus/Linear vs. Angular Speed

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Expert: Alon Mandes - 10/16/2008


Question
a patrol car is parked 50 feet from a long warehouse. 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 the following angles with the line,
perpendicular to the wall, from the light to the wall? a. theta = 30 degrees

Answer
The rate of revolving is 30, which means θ=180t where t is in sec.
Let's set x as the distance from the center of the wall, which is
the same line where the car parked. From tregonometry we know that
tan(θ)=x/50 -> x(θ)=50tan(θ). Let's substitute θ(t), we get :
x(t)=50tang[θ(t)]=50tan(180t). We are interested in finding the
speed or rate of change in x(t). So we have to derive :
x'(t)=(50*180)/cos^2(180t). Ok, when the angle is 30°, the time is :
30=180t -> t=[1/6]sec. -> x'(2)=9000cos^2(180/6)=12000ft/sec

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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