Trajectory of a free jet

In a free jet the pressure is atmospheric throughout the trajectory.

V_ox = V_o cosq = constant = V_x

V_oy = V_o sinq

x = V_ox t

y = V_oy t – gt²/2

eliminating t gives,

y = x V_oy/V_ox – gx²/(2V_ox²)

i.e,

y = x tanq – gx²/(2V_o² cos²q)

This is the equation of the trajectory.

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At the point of maximum elevation, V_y = 0 and application of Bernoulli’s law between the issue point of jet and the maximum elevation level,

V_o²/(2g) = V_ox²/(2g) + y_m

Since, V_o²/(2g) = V_ox²/(2g) + V_oy²/(2g)

we get,

y_m = V_oy²/(2g)