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Total Differentiation Problem

  1. Dec 5, 2011 #1

    D44

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    I'm trying to solve the problem but keep getting the wrong answer. Could someone help please?

    s = (v^2sin2t)/g

    where s = horizontal distance, v = initial velocity, t = angle, g = acc. gravity (9.81 m/s).

    Intended launch angle is 30 degrees, find max relative error in s if v and t are subject to relative errors of 10%.

    I've got:

    ds/dv = (2vsin2t)/g
    ds/dt = (2v^2cos2t)/g

    ds/s = 2dv/v + 2cot2t.dt

    How do I calculate this if I don't have a value of v?

    I kinda got to another step (which is still wrong I think), which is...

    ds/s = 2v/10v + (2cot(2t).dt)/10 where I thought maybe the v's cancelled.

    Any help would be appreciated.
     
  2. jcsd
  3. Dec 6, 2011 #2
    ds/s = 2dv/v + 2(cos2t/sin2t)dt
    If you consider here sin2t=x,then (cos2t dt/sin2t)=dx/x
    Hence ds/s=2dv/v+2dx/x
    substituting dv/v=10 and dx/x=10
    ds/s=40%.
    Hence relative error of s is 40%
     
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