A delta wing with sweep angle of \(45^{\circ}\) undergoes a simple harmonic plunge oscillations at \(\mathrm{M}=1.054\) at \(\mathrm{k}=0.525\). Find and plot the real part of the velocity potential 

(i) at the root, 

(ii) at \(\mathrm{y} / \mathrm{l}=0.6\), 

(iii) \(\mathrm{y} / \mathrm{l}=0.9\). 

(use 25 Mach box for half of the wing).