A steady, two-dimensional velocity field is given by \(\vec{V}=A x \hat{i}-A y \hat{j}\), where \(A=1 \mathrm{~s}^{-1}\). Show that the streamlines for this flow are rectangular hyperbolas, \(x y=C\). Obtain a general expression for the acceleration of a fluid particle in this velocity field. Calculate the acceleration of fluid particles at the points \((x, y)=\left(\frac{1}{2}, 2\right),(1,1)\), and \(\left(2, \frac{1}{2}\right)\), where \(x\) and \(y\) are measured in meters. Plot streamlines that correspond to \(C=0,1\), and \(2 \mathrm{~m}^{2}\) and show the acceleration vectors on the streamline plot.