The Amaranayaka System was a key feature of the military-administrative structure of the Vijayanagara Empire and reflected its unique political innovation.
Under this system, the empire granted land (called Amaram) to military chiefs or nobles known as Amaranayakas. In return, they were required to maintain a specified number of troops for the service of the king.
It allowed the empire to maintain a large standing army indirectly. Although the troops were maintained by Nayakas, they could be mobilized whenever needed by the central authority.
The Nayakas collected revenue from their assigned lands, a part of which funded the military, while the rest was sent to the royal treasury.
This system helped in maintaining control over far-flung territories and brought regional stability. It also integrated local chieftains into the empire’s political structure.
The Amaranayaka system was a successful model that combined feudal military service with administrative efficiency, and it played a central role in the political and military strength of the Vijayanagara Empire.

A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:
(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?