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Calc III differential

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data
    The range of a projectile fired (in a vacuum) with initial velocity V0 and inclination angle θ from the horizontal is R = (1/32) * (V0)2 * sin(2θ).

    Use differentials to approximate the change in range if V0 is increased from 400 ft/s to 410 ft/s and θ is increased from 30° to 31°.


    2. Relevant equations
    Setting up my equation:

    dR = (∂R/∂V0) * dV0 + (∂R/∂θ) * dθ


    3. The attempt at a solution
    Taking the partials and substituting values:

    sin(60°)/250 + cos(60°)/10,000 = 5216.51 ft.

    This answer seems unreasonable, can anyone check my work?
     
  2. jcsd
  3. Feb 24, 2014 #2

    SteamKing

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    It's not clear what you have done since you don't show all the steps in taking your differentials.

    Did you apply all of the derivative rules correctly? I can't tell from the attempt at your solution, since you have already substituted numbers. What happened to the factor (1/32) from the original range equation?
     
  4. Feb 24, 2014 #3
    The attempt at a solution:

    Taking the partials:

    ∂R/∂V0 = (sin(2θ)*V0)/16

    ∂R/∂θ = (cos(2θ)*(V0)2)/16

    dV0 = 10

    dθ = 1

    I then substituting and simplified.
     
  5. Feb 24, 2014 #4

    SteamKing

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    Did you use radian measure for your dθ?
     
  6. Feb 24, 2014 #5
    I thought I had calculator in degree mode, however I went back through with radian and verified d(theta) was in radians.

    Also there was a sign error in my calculations so the new answer is 129.24 ft which seems more reasonable don't you think?
     
  7. Feb 24, 2014 #6

    SteamKing

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