A syringe containing water is held horizontally with its nozzle at a height h above the ground as shown in fig the cross sectional areas of the piston and the nozzle are A and a respectively the piston is pushed with a constant speed v. Find the horizontal range R of the stream of water on the ground.

Explanation

Let v' be the horizontal speed of water when it emerges from the nozzle then from equation of continuity
`Av=av'impliesv'=(Av)/a`
Let t be the time taken by the stream of water to strike the ground then `h=1/2 "gt"^(2)`
`implies t=sqrt((2h)/t)implies` horizontal distance
`R=v'sqrt((2h)/g)=(Av)/a sqrt((2h)/g)`