Sand is being dropped from a stationary dropper at a rate of 0 ....

When the sand is dropped on the conveyor belt its velocity will become equal to that of the conveyor. Therefore, $v = 5m{s}^{- 1}$.

The force required to keep the conveyor belt moving will be equal to the gain in the momentum by the sand per second.

$⇒ F = \dfrac{d m}{d t}v ⇒ F = 0 . 5 \times 5 = 2 . 5N$

Now the power required to keep the conveyor belt moving will be,

$P = Fv ⇒ P = 2 . 5 \times 5 = 12 . 5W .$