Calculus/calculus 1

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Expert: Alon Mandes - 11/13/2009


Question
A boat leaves the dock at 2 pm. and travels due south at a speed of 20mph. Another boat, which had been heading due east at 15 mph, arrives at the dock at 3 pm. At what time were the 2 boats closest together?

Answer
Let's set this time as to . After 1 hour boat B arrived to the dock. That means that at 2pm
after to minutes, boat A travelled 20to %26 boat B travelled 15to .
boat B where 15 mile away from the dock. Now, according to Pythagoras : the distance L
between the boats at time t=to is : L=√[(20to)²+(15-15to)²]=√[400to²+225(1-to)²] . To obtain
minimum , we solve L'(to)=0 : L'=[800to-450(1-to)]/2√[400to²+225(1-to)²] .
L'=0 --> 800to-450(1-to)=0 --> 16to-9(1-to)=0 --> 16to-9+9to=0 --> 25to=9 --> to=9/25=0.36 -->
After 21.6 minutes from 2pm the distance was minimum.

Alon.

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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