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Calculus/can u help me find the answer for this questions?

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Expert: Alon Mandes - 9/26/2010


Question
Find the point on the curve r(t) = (5 sin t)ı + (5 cos t) +
12tk at a distance
26π units along the curve from the point (0, 5, 0) when t = 0
in the direction
of increasing arclength.

Answer
Ok Farah , let's review our facts :
1. Our trajectory is r(t#=[5Sin#t#,5Cos#t#,12t]
  Or in other form : x#t#=5Sin#t# , y#t#=5Cos#t# , z#t#=12t .
2. Our initial point AND final point are : [0,to]
3. The arc length from 0 to to is 26π
4. The formula for arc length is :
 to         to  
L=∫|r'#t#|dt=∫ √{ [x'#t#]² + [y'#t#]² + [z'#t#]² } dt
 0          0

In our case : x'#t##5Cos#t# , y'#t##-5Sin#t# AND z'#t##12 .
Thus,

   to
26π#∫ √{ 25Cos²#t# + 25Sin²#t# + 144 } dt
   0
   to                   to          to
26π#∫ √{ 25 + 144 } dt # ∫√{169}dt # ∫13dt # 13to     
   0                    0           0

So, 26π#13to --> to#26π/13 .
The point is :
[5Sin#26π/13#,5Cos#26π/13#,312π/13]

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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