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Math Help - velocity question

  1. #1
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    velocity question

    Hi I need help with this question:

    A steam catapult aboard an aircraft carrier can accelerate an F-18 Hornet so that its velocity is given by

    v(t) = 104.85t feet/second

    If the jet reaches its take-off velocity of 173 miles per hour at the end of the runway, how long does it take for the jet to take off?

    __________ seconds.

    How long is the runway?
    __________ feet

    I figured out that I needed to convert mph to feet per second which is:

    173mph to 253.7333 fps

    And this is where I get stuck I don't know what to do.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by killasnake View Post
    Hi I need help with this question:

    A steam catapult aboard an aircraft carrier can accelerate an F-18 Hornet so that its velocity is given by

    v(t) = 104.85t feet/second

    If the jet reaches its take-off velocity of 173 miles per hour at the end of the runway, how long does it take for the jet to take off?

    __________ seconds.

    How long is the runway?
    __________ feet

    I figured out that I needed to convert mph to feet per second which is:

    173mph to 253.7333 fps

    And this is where I get stuck I don't know what to do.
    v=104.85 t ft/s.

    Take-off speed is 253.733 ft/s, and so the plane reaches this speed
    when:

    104.85 t=253.733,

    or:

    t=253.733/104.85 seconds.

    RonL

    (aside: there is no such aircraft as the f-18, probably f/a-18 Hornet is meant)
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  3. #3
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    Thank you for the help
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  4. #4
    Forum Admin topsquark's Avatar
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    You know, I read Malaygoel's post and whereas it wasn't very specific, it WAS the method for solving for the length of the runway. I wouldn't have called it "totally useless."

    -Dan
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  5. #5
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    Well, One more question

    Now know how long the take off speed is which is 2.41996 How do I figure out how long the runway is?
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  6. #6
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    Quote Originally Posted by killasnake View Post
    Well, One more question

    Now know how long the take off speed is which is 2.41996 How do I figure out how long the runway is?
    Since you posted this in the Calculus section, you use the integration as suggested before.

    v(t) = dS/dt
    where
    v(t), read "v of t" or "v as a function of t", is velocity.
    S is distance
    t is time

    So, as given,
    dS/dt = 104.85t
    Multiply both sides by dt,
    dS = 104.85t dt
    Integrate both sides,
    S = (104.85)[(t^2)/2]
    Hence if t = 2.41996 sec,
    S = (104.85 /2)(2.41996^2) = 307 ft., the length of the runway ---answer.

    --------------------
    If you want to check that via linear kinematics or physics,
    You know distance is (average speed) times time
    d = [(v1 +v2)/2]*t

    Here,
    v1 = initial speed = 0
    v2 = speed at takeoff = 253.7333 ft/sec
    t = 2.41996 sec
    So,
    d = [(0 +253.733)/2]*(2.41996) = 307 ft. ---same.
    Last edited by ticbol; September 15th 2006 at 09:37 PM. Reason: ft, not meters
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