Find the distance the container is lifted as the winch is rotated through an angle of 5pi/6 radian and a having a radius of 6 in
one complete rotation moves the container a distance equal to the circumference of the winch spool.
one complete rotation is 2pi radians.
5pi/6 radians is thus (5pi/6)/(2pi) = 5/12 of a complete rotation.
the circumference is 2pi*6 = 12pi inches, so the container is lifted (5/12)(12pi) = 5pi inches.
To find the distance the container is lifted (also known as the vertical displacement), we can use the formula for the arc length of a circle.
The arc length, denoted as "s", is given by the equation:
s = r * θ
where:
s is the arc length,
r is the radius of the circle,
and θ is the angle (in radians) subtended by the arc.
In this case, the radius of the winch is given as 6 inches and the angle through which it is rotated is 5π/6 radians.
Therefore, we can substitute these values into the formula and calculate the distance the container is lifted:
s = 6 inches * (5π/6 radians)
s = 5π inches
So, the container is lifted by a distance of 5π inches.