Answer
$\approx 6.7$ ft/s
Work Step by Step
Suppose a point moves along a circle of radius $r$
and the ray from the center of the circle to the point
traverses $\theta$ radians in time $t$.
Let $ s=r\theta$ be the distance the point travels in time $t$.
The angular speed of the point is $\omega=\theta/t$.
The linear speed of the point is $v=s/t$.
$ v=r\omega$.
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The load rises with the linear speed of a point on the winch arc.
1 revolution = $ 2\pi$ radians.
$\displaystyle \omega=\frac{\theta}{t}=\frac{8\cdot 2\pi\ rad}{15\ s}=\frac{16\pi}{15}$ rad/s
$ v=r\displaystyle \omega=2\cdot\frac{16\pi}{15}\approx$6.70206432766
$\approx 6.7$ ft/s
