Final answer:
The question requires understanding of fluid dynamics and projectile motion to calculate the horizontal distance a syringe ejects liquid. It involves using the speed of the piston, the diameters of the syringe and nozzle, and the height from the ground to find the time of flight and the horizontal range.
Step-by-step explanation:
The question involves applying principles from physics, specifically fluid dynamics, to calculate the horizontal distance a liquid travels when ejected from a syringe. By using the continuity equation and equations of motion, we can determine the speed at which the liquid leaves the nozzle and then calculate the time it takes for the liquid to fall to the ground due to gravity. If we assume ideal conditions and that the liquid behaves as a projectile in horizontal motion, the only force acting on it after leaving the nozzle is gravity; hence there is no horizontal acceleration. The horizontal distance traveled by the liquid jet can thereby be calculated using projectile motion equations.
However, as the detailed solution is not provided, it's clear that to solve it, one would need to find the exit velocity of the liquid using the given speed of the piston and the diameters of the syringe and nozzle, then use this exit velocity to determine the horizontal range of the liquid, applying the formula for projectile motion where horizontal range R = (velocity×time), and time is derived from (2×height)/g, considering g as the acceleration due to gravity.