Question 1134297
.
<pre>
The formula   S = {{{r*alpha}}}  for the arc length  " S "  via the radius " r " and the central angle  " {{{alpha}}} "  (in radians) works  

in both cases  when  the angle {{{alpha}}}  is between 0 and {{{2*pi}}}  and when the angle {{{alpha}}}  is greater (larger) than {{{2*pi}}},  describing many rotations.


For the first question, the arc length is 1 meter, the radius  r = {{{0.35/2}}} = 0.175 meters.


So, the angle  the handle turn in winding up 1 m of the rope is


    {{{alpha}}} = {{{1/r}}} = {{{1/0.175}}} = 5.714 radians = 329 degrees.    <U>ANSWER</U>




For the second question, you may continue through this way, but more short way is to use a proportion 


    {{{11/x}}} = {{{0.175/0.42}}}


to find the distance " x "  the handle of the winder travel when bringing the bucket up 11 meters from the bottom.


From the proportion,  x = {{{(11*0.42)/0.175}}} = 26.4 meters.     <U>ANSWER</U>
</pre>