A wind blows toward a hill arising from a plain that can be approximated with the top section of a half$-$body. The wind has a uniform velocity $U_0=20\frac{m}{s}$ far ahead of the hill. The height of the hill, $h,$ approaches $100$ m $.$ Air density is $1\mathrm{.}2k\frac{g}{m^3}.$ Point $(3)$ is on the hill and directly above the origin. Use the half$-$body potential flow to determine: $($a$).$ The elevation of point $(3)$ above the plain.

$($b$).$ The magnitude of the air velocity at point $(3)?$

$($c$).$ The difference in pressure between point $(2)$ and point $(3)?$