Find the inverse of the particle paths given in Problem 10.9. Find the initial position of the particle located at (2m, 0, 0) at t = πs. Problem 10.9 The Lagrangian particle paths for an irrotational...

Find the inverse of the particle paths given in Problem 10.9. Find the initial position of the particle located at (2m, 0, 0) at t = πs.

Problem 10.9

The Lagrangian particle paths for an irrotational vortex are given by

where K is a constant in m²
/s. Where will the particle located at R₀
= 1m, θ₀
= 0, Z₀
= 0 at t₀
= 0, be at t = πs?