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Math Help - Sorry to ask another question, but I need help with trig functions!

  1. #1
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    Sorry to ask another question, but I need help with trig functions!

    The question:
    When you use a sewing-machine, the needle moves in relation to the sewing plate (where the clothe is). To the time t, the needle's height y(t) over the sewing-plate is decided by:

    y(t)=\frac 32 \cdot sin(12\pi t)

    Where t is meazured in seconds and y(t) is meazured in centimeters.

    The needle's velocity to the time t is y'(t). What is the velocity of the needle when it passes the sewing-plate?

    I found the y'(t) previously with the help from you guys:

    y'(t)=\frac 32 \cdot 12 \pi \cdot \cos(12 \pi t)

    But what now? I'm a bit lost.
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  2. #2
    Super Member 11rdc11's Avatar
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    I'm kind of confused by the question. If it is asking what the velocity of the needle is when touching the plate you would find t by

    0=\frac 32 \cdot sin(12\pi t)

    Once you find t then plug it in your velocity function.
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  3. #3
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    Well you know on a sewing machine, there is this plate where you put the clothes on, and then the needle goes down into the clothes and into this plate. I need to calculate the velocity of the needle when it goes through this plate.

    I would set y(t) to zero as well, but it confuses me when it says that y'(t) is the velocity?
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  4. #4
    Super Member 11rdc11's Avatar
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    Ok then the way I told you is correct. The first function is your position function y(t). The position function tells you the height of the needle for any t, t being time. I set the position function to 0 becuase that would be when the needle is touching the plate.

    Now y'(t) is your velocity function and tells you the velocity for any t.

    Ok so find out what t makes the position equal to 0

    0=\frac 32 \cdot sin(12\pi t)

    So when you solve for t you will find at what time the needle is touching the plate

    Now take your value for t and plug it in to your velocity function and it will tell you what the velocity is at the time the needle is touching the plate.
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  5. #5
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    The way to solve this question is to calculate y'(t_1), where t_1 is the time at which the needle hits the plate. That time is calculated by 0 = \frac{3}{2}\sin {(12\pi{t_1})}. In other words, at what time is the sine equal to zero? A very simple answer is when t = 0. Therefore, to answer the question of velocity, you solve for y'(t) by substituting t = 0 into the velocity equation.
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  6. #6
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    Okay, thanks both of you. You are both saying the same, which is to find the value of t in the first equation when y(t) = 0, and then substitute t in the differentiated equation with the value I have found.

    0=\frac 32 \cdot sin(12\pi t)

    \frac 0{\frac 32}=sin(12\pi t)

    12\pi t=sin^{-1} (0)

    t = \frac 0{12\pi}

    t=0

    And so t is has the value 0. Then 0 substitutes t in the velocity equation:

    y'(t)=\frac 32 \cdot 12 \pi \cdot \cos(12 \pi \cdot 0)

    y'(t)=\frac 32 \cdot 12 \pi \cdot \cos(0)

    y'(t)=\frac 32 \cdot 12 \pi \cdot 1

    y'(t)=56.55

    So that is basically the velocity, right?

    One last question, is my answer then 56.55 cm/seconds?
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  7. #7
    Super Member 11rdc11's Avatar
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    Yep that's the right answer and yes \frac{cm}{s}
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  8. #8
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    Thanks a whole bunch
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