The piston and nozzle of a syringe kept horizontal have diameters 5 mm and 1 mm. the piston is pushed with constant velocity of 0.2ms^(-2) Find the horizontal distance travelled by water jet before touchig water[g=10m//s^(2)]. Height of syringe from ground is 1 m.

The piston and nozzle of a syringe kept horizontal have diameters 5 mm

1.	The piston and nozzle of a syringe kept horizontal have diameters 5 mm and 1 mm. the piston is pushed with constant velocity of 0.2ms^(-2) Find the horizontal distance travelled by water jet before touchig water[g=10m//s^(2)]. Height of syringe from ground is 1 m.
Answer» Solution :`d_(1)=5mmthereforer_(1)=2.5mm=2.5xx10^(-3)m` `d_(2)=1mmthereforer_(2)=0.5mm=0.5xx10^(-3)m` If velocity of water coming out of a SYRINGE is `v_(2)` , according to CONTINUITY equation , `A_(1)v_(1)=A_(2)v_(2)` `thereforev_(2)=((A_(1))/(A_(2)))v_(1)` `=((pir_(1)^(2))/(pir_(2)^(2)))v_(1)=((r_(1))/(r_(2)))^(2)v_(1)` `=((2.5)/(0.5))^(2)xx0.2(becausev_(1)=0.2m//s))` `thereforev_(2)=5m//s`. Time taken by water jet when it touches the ground using. `d=(1)/(2)g t^(2)` `1=(1)/(2)xx10t^(2)(d=1.0m)` `thereforet=(1)/(sqrt(5))s` `therefore`Horizontal distance covered by water jet in time t is , `x=v_(2)t=5xx(1)/(sqrt(5))` `thereforex=sqrt(5)m`. `thereforex=2.23m`.