Jet trajectory from a free nozzle into air: When a liquid issues horizontally from a nozzle into the atmosphere (neglecting air resistance close to the nozzle), what is the ideal shape of the jet path under gravity?

Introduction / Context:
Once a jet leaves a nozzle and is exposed to the atmosphere, it behaves like a continuous stream of fluid particles subjected mainly to gravity. Close to the nozzle (neglecting aerodynamic breakup), each fluid particle follows projectile motion principles.

Given Data / Assumptions:

• Jet issues horizontally at speed u from a nozzle into still air.
• Air resistance is neglected over the short distance of interest.
• Gravity g acts downward; initial vertical velocity is zero.

Concept / Approach:

Projectile motion under constant gravitational acceleration produces a parabolic path. The horizontal velocity component remains constant (u), while the vertical component increases linearly with time (g t). Eliminating time yields y = (g x^2) / (2 u^2), the equation of a parabola in x–y coordinates.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: y has dimensions of length; expression (g/u^2) x^2 is consistent. Observationally, short horizontal jets (e.g., water taps) display a parabolic profile before breaking into droplets.

Why Other Options Are Wrong:

(a) would require zero gravity; (b) and (c) require centripetal constraints not present; (e) does not arise from uniform gravity with constant horizontal speed.

Common Pitfalls:

Including significant air drag near the nozzle; forgetting the vertical initial velocity is zero for a horizontal jet.

Final Answer:

parabolic trajectory