Arc Length, Cargo problem

on3winyoureyes

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Jan 20, 2015
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A cargo winch is 3 ft in diameter. Through which angle (in degrees) will the winch be able to lift an object 25 ft.?

My work:
r=1.5 ft
d=feet
I think we use the arc length formula
so it'd be
theta=d/r = d/1.5 and so 25ft/1.5
so it'd be 16.67 degrees?
 
A cargo winch is 3 ft in diameter. Through which angle (in degrees) will the winch be able to lift an object 25 ft.?

My work:
r=1.5 ft
d=feet
I think we use the arc length formula
so it'd be
theta=d/r = d/1.5 and so 25ft/1.5
so it'd be 16.67 degrees?

Almost correct!

The unit of rotation is in radian. So the rotation of the winch is 50/3 radians. Now you need to convert it to degrees, using 180° = π radians.
 
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