The manganate ion (\({MnO_4^{2-}}\)) undergoes a disproportionation reaction in an acidic medium.
In this reaction:
Reaction:
\[ 2{MnO_4^{2-}} + 4{H^+} \rightarrow {MnO_4^-} + {Mn^{2+}} + 2{H_2O} \]
When potassium permanganate (\({KMnO_4}\)) is heated, it decomposes to form potassium manganate (\({K_2MnO_4}\)) and oxygen gas.
Reaction:
\[ 2{KMnO_4} \xrightarrow{\text{heat}} {K_2MnO_4} + {O_2} \]
This is a decomposition reaction that releases oxygen and forms a green manganate salt.

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?