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  1. MHB Apprentice

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    #1
    A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?


    so, I am new to kinomatic equations. We are using the 4 Basic ones.

    need to see this one worked out if I may.


    Thanks

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  3. Indicium Physicus
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    #2
    What is the target variable? That is, what is it for which you're trying to solve?

  4. MHB Apprentice

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    #3 Thread Author
    distance?

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    #4
    What is it that you are given? And how may we relate these values?

  6. Indicium Physicus
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    #5
    Another way of saying what MarkFL said is this: can you write down a relevant, correct equation involving the target variable of distance?

  7. MHB Apprentice

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    #6
    Quote Originally Posted by mathkid3 View Post
    A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?


    so, I am new to kinomatic equations. We are using the 4 Basic ones.

    need to see this one worked out if I may.


    Thanks
    I think the OP meant the kinematic equations, 4 basic ones meaning:

    1) x=x0+V0t+1/2at2
    2) V=V0+at
    3) a=constant
    4) V2=V02+2a(x-x0)

    If this is the case, the answer is a matter of determining starting values.

    We can assume that the plane starts off at point 0 on the runway meaning that x0=0. we can also assume that the plane's initial velocity is 0, V0=0 (before moving). now we are given the acceleration, a=3.8m/s2, and final velocity, V=33m/s. From this we can find how long it will take the plane to reach the final velocity, using equation 2:

    33m/s=0+(3.8m/s2)t
    t=(33/3.8)s

    Now that we have a value for t, we can use equation 1 to find the total runway length, x, required to reach takeoff speed:

    x=0+0(t)+1/2at2
    =(1/2)(3.8m/s2)((33/3.8)s)2
    =143.30m

    therefore the minimum amount of runway needed to reach the plane's necessary takeoff speed is 143.30 meters.

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