Prob. $4\mathrm{.}1\mathrm{.}14$ p$.$ IP$-48.$

$4\mathrm{.}1\mathrm{.}14$ WP In addition to the customary horizontal velocity components of the air in the atmosphere $($the "wind"$),$ there often are vertical air currents $($thermals$)$ caused by buoyant effects due to uneven heating of the air as indicated in Fig. P$4\mathrm{.}1\mathrm{.}14.$ Assume that the velocity field in a certain region is approximated by $u=u_0,v=v_0(1-\frac{y}{h})$ for $u=u_0,v=0y>h\frac{u_0}{v_0}=0\mathrm{.}5,10,$ and $u=u_0,v=0$ for $y>h.$ Plot the shape $of$ the stream line that passes through the origin for values $of\frac{u_0}{v_0}=0\mathrm{.}5,1,$ and $2$