Answer
$v\sqrt {\frac{2h}{g}}$
Work Step by Step
Please see the attached image first.
Let's apply the equation $S=ut+\frac{1}{2}at^{2}$ to the product to find the time of motion.
$\downarrow S=ut+\frac{1}{2}at^{2}$
Now plug known values into this equation.
$h= (0)t +\frac{1}{2}gt^{2}$
$\frac{2h}{g}=t^{2}\space=\gt t=\sqrt {\frac{2h}{g}}$
Let's apply the equation $S=ut$ to the box to find the distance from the bottom of the robot arm.
$\rightarrow S=ut$
$S=v\times \sqrt {\frac{2h}{g}}= v \sqrt {\frac{2h}{g}}$
