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Math Help - Word Problem need helpp !!

  1. #1
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    Word Problem need helpp !!

    The world's largest four faced chiming clock is in London. The face of the clock is 7m in diametre, the minute hand is 4.3m and the hour hand is 2.7m LONG

    1) Find the linear speed of the tip of the minute hand and the tip of the hour hand of the clock

    2) If t is the angle described by the hands @ 4:00 taking the intial side of the angle to be the minute hand and the terminal side to be the hour hand, then what are the values of sin(t) and cos(t)


    Can anyone help me with these questions? Thank you
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  2. #2
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    Linear spped is given by \frac{{\Delta}s}{{\Delta}t}

    The tip of the minute hand travels 2{\pi}(\frac{43}{10})=\frac{43\pi}{5} meters per 60 minutes.

    It's linear speed is then \frac{\frac{43\pi}{5}}{60}=\frac{43\pi}{300} meters per minute.

    Can you figure out the hour hand?. Remember 12*60=720.

    The angle swept out from the minute hand at 12 and the hour hand at 4 is \frac{4\pi}{3}.
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  3. #3
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    i don't get the part where u said 12*60=720 and
    The angle swept out from the minute hand at 12 and the hour hand at 4 is .
    Can u please explain to me?
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  4. #4
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    The angle swept out from the minute hand at 12 and the hour hand at 4 is .
    The numbers are placed evenly around the circumference of the clock. So the 4 is \frac{4}{12} of the way round.
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  5. #5
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    London clock

    i read this problem shortly after it was posted. it appeared too simple.when i noticed that the long hand was longer than the clock radius i decided not to reply.there still appears to be some confusion.
    i offer the following
    a trig function of any angle will equal plus or minus that same function of the corresponding acute angle.the corresponding acute angle of 120 degrees is 60 degrees and the angle is in the second quartrant where x is negative and y positive. sign of 60 is .866, cosine is -.5
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  6. #6
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    bjhopper,
    im not really clear with what you said..><'''
    this question is really confusing mee...
    can anyone else help explain?
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  7. #7
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    london clock

    problem with linear speeds ?
    problem with trig functions for angles greater than 90 degrees?
    if latter then you need to learn how to convert these angles into corresponding acute angles.suggest you go into google for trigonometric functions.there are various web sites explaining how this is done on a coordinate diagram using a unit circle at 0,0


    bj
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  8. #8
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    im confused with the linear speeds..question #1 in particular
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  9. #9
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    london clock

    radius of clock is 3.5 m.long hand should be shorter than that. lets say its 3.4 m
    tips of hands travel along concentric circles each with a radius equal to the hands length. each complete revolution travels a distance 2 pi r
    long hand 2pi3.4 or 21.4m. short hand 2pi2.7 or 17 m.
    long hand makes one rev every 60 minutes, speed is 21.4 /60 =.36m/min
    short hand makes one rev every 12 hrs or 720 min. speed is17/720=.024 m/min


    bj
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