The problem can be represented diagrammatically as follows:

We can see that the length of the major axis is 8m, and the minor axis is 4m.

$2a = 8 \rightarrow a = 4$ and $b = 2 \rightarrow b = 2$.

Therefore the equation of the semi-ellipse is $\large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2} $$ = 1, y \geq 0 \rightarrow \large\frac{x^2}{16}$$+\large\frac{y^2}{4} $$ = 1$

We need to find $AC$, given $AB = 1.5m$.

$x$ coordinate of point $C$ is $2.5\;$i.e., $(OB - AB = 4 - 1.5 = 2.5)$

$\Rightarrow y\;$ coordinate (AC) $= \large\frac{2.5^2}{16}$$+\large\frac{y^2}{4}$ $ = 1 \rightarrow y^2 = \large\frac{16-6.25}{4}$$ = \large\frac{9.75}{4} $$ \rightarrow y \approx 1.56$