At a surprise party for a friend you've tied a series of \(20-\mathrm{cm}-\) diameter helium balloons to a flagpole, each tied with a short string. The first one is tied \(1 \mathrm{~m}\) above the ground, and the other eight are tied at \(1 \mathrm{~m}\) spacings, so that the last is tied at a height of \(9 \mathrm{~m}\). You notice that in the steady wind, each balloon is blown by the wind so it looks like the angles that the strings make with the vertical are about \(10^{\circ}, 20^{\circ}, 30^{\circ}, 35^{\circ}, 40^{\circ}, 45^{\circ}, 50^{\circ}, 60^{\circ}\), and \(65^{\circ}\). Estimate and plot the wind velocity profile for the 9-m range. Assume the helium is at \(20^{\circ} \mathrm{C}\) and \(10 \mathrm{kPa}\) gage and that each balloon is made of \(3 \mathrm{~g}\) of latex.