A canon can fire shells at speed u. Inclination of its barrel to the horizontal can be changed in steps of `Delta theta = 1^(@)` ranging from `theta_(1) = 15^(@)` to `theta_(2) = 85^(@)`. Let `R_(n)` be the horizontal range for projection angle `theta = n^(@)`.
`Delta R_(n) = |R_(n) - R_(n+1)|`
For what value of n the value of `DeltaR_(n)` is maximum? Neglect air resistance.
(ii) A small water sprinkler is in the shape of a hemisphere with large number of uniformly spread holes on its surface. It is placed on ground and water comes out of each hole with speed u. Assume that we mentally divide the ground into many small identical patches – each having area `DeltaS`. What is the distance of a patch from the sprinkler which receives maximum amount of water ?

Answer

(i) `n = 84^(@)` (ii) `(u^(2))/(g)`