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Question

Water is filled in a uniform container of the area of cross section A. A hole of cross-section area a (<< A) is made in the container at a height of 20 m above the base. Water streams out and hits a small block placed at some distance from the container. With what speed (in ms1) the block should be moved such that water streams always hits the block. (Given aA=120). (Take g=10ms2)

 


Solution

Velocity of efflux v=2gy
Range x=2gy×2hg
The velocity of the block must be (dxdt).
Vb=dxdt=2hg×2g×12ydydtVb=hy.dydt     ...(i)
Using equation of continuity
Adydt=a2gy     ...(ii)
equation (i) and (ii) 
Vb=hy×aA2gyVb=2gh×ah=20×120=1 ms1


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