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Math Help - Differential Equation Problem Jet Take Off

  1. #1
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    Differential Equation Problem Jet Take Off

    I really can't figure out this problem nor can i figure a similar problem from an example in class.

    Suppose a particular jet needs to attain a speed of 220 mph to take off. If it can accelerate from 0 to 220 mph in 45 seconds, how long must the runway be(in feet)? Assume constant acceleration. Note: 1 mph = 22/15 ft/sec.

    Thanks!
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by ishanj07 View Post
    I really can't figure out this problem nor can i figure a similar problem from an example in class.

    Suppose a particular jet needs to attain a speed of 220 mph to take off. If it can accelerate from 0 to 220 mph in 45 seconds, how long must the runway be(in feet)? Assume constant acceleration. Note: 1 mph = 22/15 ft/sec.

    Thanks!
     <br />
\frac{d^2y}{dt^2}= a<br />
     <br />
\frac{dy}{dt}=\int{adt}=at<br />
     <br />
y=\int{atdt}=at^2/2<br />
    hence
     <br />
y= \frac{(220-0)*22/15}{45} * {45}^2= ans<br />
    That's your answer!
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  3. #3
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    Quote Originally Posted by ADARSH View Post
     <br />
\frac{d^2y}{dt^2}= a<br />
     <br />
\frac{dy}{dt}=\int{adt}=at {\color{red}+ C}<br />

    But dy/dt = 0 when t = 0 therefore C = 0.

     <br />
y=\int{atdt}=at^2/2 {\color{red}+ D}<br />

    But y = 0 when t = 0 therefore D = 0.

    hence
     <br />
y= \frac{(220-0)*22/15}{45} * {45}^2= ans<br />
    That's your answer!
    Mr F edits in red.

    I'm sure you did this in your head but best to spell it out .... the arbitrary constant often gets forgotten - a disaster when it's not equal to zero
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  4. #4
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    Don't forget to divide the answer given above by 2 which comes when you take the anti derivative of the acceleration*time in the second integral.

    If you don't, the answer you get above will be 14520 feet, which is incorrect.
    (at^2) = 14520 (INCORRECT!)

    Divide by 2 and you will have the correct answer:
    (at^2)/2 = 7260 (CORRECT!)
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