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Math Help - Setting up problem.

  1. #1
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    Exclamation Setting up problem.

    A railroad track is laid along the arc of a circle of radius 1800. The circular part of the track subtends a central angle 40 degrees. How long in Sec will it take s point on the front of the train moving at 30 mph to go around this portion.
    I'm given: Radius-1800 Theta-40 Velocity-30. So, would I use V=r(theta)/time. Then, divide by 60 time to convert to seconds.
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  2. #2
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    Hint: length of arc = 40/360 * pi(2*1800) = pi(3600) / 9 = ?
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  3. #3
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    Still does not really help me out.
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  4. #4
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    Quote Originally Posted by Brndo4u View Post
    A railroad track is laid along the arc of a circle of radius 1800. The circular part of the track subtends a central angle 40 degrees. How long in Sec will it take s point on the front of the train moving at 30 mph to go around this portion.
    I'm given: Radius-1800 Theta-40 Velocity-30. So, would I use V=r(theta)/time. Then, divide by 60 time to convert to seconds.
    Your speed is given in miles per HOUR -- 3600 seconds in a hour.

    You can determine the arc length: 400 \pi feet.
    (Wilmer gave you that -- I just did the division of 3600 by 9 to leave 400.)

    The speed: 30 mph is equivalent to:

    \dfrac{ 30 miles/hour \cdot 5280 feet/mile}{3600 seconds/hour} =  \dfrac{44 feet}{second}

    Then divide the arc length by the speed:

     \dfrac{ 400 \pi \, feet }{44 feet / second} to get the time in seconds to traverse the arc.
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  5. #5
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    OK; rounding out:

    Arc length = 400*pi = 1257 MILES (if the given 1800 is in miles; IS IT?)

    1257 / 30 mph = 42 HOURS

    42 * 60 * 60 = 151,200 SECONDS.

    In other words, your problem makes little sense.
    Are you sure you entered it correctly?
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