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Math Help - Radian word problems- Ugrent

  1. #1
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    Radian word problems- Ugrent

    The revoling restauraunt in the CN Tower completes 5/6 of a revolution every hour. If two people ate dinner from 19:15 to 21:35, through what angle did there table rotate during the meal. Express your anwser in radian measure in exact form and in appoximate form, to the nearest tenth.

    Also
    A ferris wheel with a radius of 32m makes 2 revolutions every minute.
    a) find the anglular volocity, in radians per second
    b) if the ride last 3 min, how far does the ride travel, to the nearest meter?

    Thanks so much
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  2. #2
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    Quote Originally Posted by musicismylife2007 View Post
    1) The revoling restauraunt in the CN Tower completes 5/6 of a revolution every hour. If two people ate dinner from 19:15 to 21:35, through what angle did there table rotate during the meal. Express your anwser in radian measure in exact form and in appoximate form, to the nearest tenth.

    2) Also
    A ferris wheel with a radius of 32m makes 2 revolutions every minute.
    a) find the anglular volocity, in radians per second
    b) if the ride last 3 min, how far does the ride travel, to the nearest meter?

    Thanks so much
    Hello,

    to 1)

    1. Time difference: 21:35 - 19:15 = 2 h \ 20 min = \frac73\ h

    2. Calculate the number of revolutions: \frac73\ h \cdot \frac56\ \frac{rev}{h}=\frac{35}{18}\ rev

    3. Calculate the angle: \left \{\begin{array}{l}1\ rev\ \longmapsto\ 2\pi\\ \frac{35}{18}\ rev \ \longmapsto\ \boxed{\frac{35 \pi}{9} \approx 12.2} \end{array}\right.

    to 2)
    a) 2 revolutions in 1 minutes correspond with 4\pi in 60 seconds. Thus the angular velocity is:

    \omega = \frac{4 \pi}{60\ s}=\frac{\pi}{15}\ s^{-1}

    b)In 3 minutes the wheel has done 6 revolutions. The distance covered by 1 revolution is: p=2 \pi\ \cdot 32\ m=64 \pi \ \frac{m}{rev}. Thus the total length of the ride is:

    r = 6\ rev \cdot 64 \pi \ \frac{m}{rev}=384 \pi\ m \approx 1206\ m
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