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Math Help - Angles, Bearings and Angular Velocity

  1. #1
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    Angles, Bearings and Angular Velocity

    City X is 85 miles due south of City Y, and City Z is 15 miles due west of City X. What is the bearing of City Z from City Y?

    Bearing means angle right? How do I find th angle that corresponds there?

    A boat sails for 3 hours at 15 mph in a direction 10517'. How far south has it sailed?

    The way I see it, a boat has been sailing somewhat NNW for 45 miles... how do I determine how far south it's gone?

    Two pulleys of diameter 6 m and 3 m are connected by a belt. The larger pulley rotates 41 times per min. Find the angular speed of the smaller pulley.

    V = rw and w = theta/t

    how do I find theta to plug in my formula?
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  2. #2
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    Quote Originally Posted by juangohan9
    City X is 85 miles due south of City Y, and City Z is 15 miles due west of City X. What is the bearing of City Z from City Y?
    Code:
          Y
          |
          |
          |
    Z---X
    I think it is 270.
    Because the way bearings work (I think) is just like angles except they are measured clockwise. So that angle from Y to Z is 270 degreees.

    A boat sails for 3 hours at 15 mph in a direction 10517'. How far south has it sailed?
    Code:
         +----------- 
        / |
       /  |  
      /   |  
     /    |
    The slanted line forms an angle of 105 degrees and 17 minutes. What you seek is length of the vertical line. The the angle between the slanted and the vertical is,
    \theta=104^o 77'-89^o 60'=15^o 17'
    Then,
    \cos 15^o 17' = \frac{x}{\mbox{hypotenuse}}
    But the hypotenuse is the length of the slanted line. Which is 45 miles because the ship is traveling at 15 miles per hour for 3 hours. And x is the length of the vertical line.
    Thus,
    x=45 \cos 15^o 17'\approx 43.41
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  3. #3
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    Quote Originally Posted by juangohan9
    Two pulleys of diameter 6 m and 3 m are connected by a belt. The larger pulley rotates 41 times per min. Find the angular speed of the smaller pulley.

    V = rw and w = theta/t

    how do I find theta to plug in my formula?
    The two pulleys are connected by a belt. This means that the belt goes over both of them with the same linear speed. Thus both pulleys have the same linear speed on their surfaces.
    v_L = v_R (L is the "large" pulley and S is the "small" pulley.)

    r_L \omega_L = r_S \omega_S

    \omega_S = \frac{r_L}{r_S} \omega_L = \frac{6}{3} \cdot 41 = 82 rot/min.

    -Dan
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  4. #4
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    Quote Originally Posted by juangohan9
    ...
    A boat sails for 3 hours at 15 mph in a direction 10517'. How far south has it sailed?
    ...
    Hello,

    usually bearings are measured clockwise from the north. If the "direction" in your problem is meant to be a bearing then the boat is running nearly to ESE.

    I've attached a diagram to demonstrate the situation. The line indicated in blue is the way south.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Angles, Bearings and Angular Velocity-bearings1.gif  
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