Here, width of elliptical arch = 8 m
∴ AB = 8 m ⇒ 2a = 8 ⇒ a = 4
Height at the centre = 2 m
∴ OC = 2 ⇒ b = 2
The axis of the ellipse is x-axis. So the equation of ellipse in standard form is

x2

a2

+

y2

b2

= 1.

∴

x2

(4)2

+

y2

(2)2

= 1 ⇒

x2

16

+

y2

4

= 1
Now, AP = 1.5 m
OP = OA – AP = 4 – 1.5 = 2.5 m
Let PQ = h m
∴ Coordinates of Q are (2.5, h)
Since the point Q lies on the ellipse

x2

16

+

y2

4

= 1
∴

(2.5)2

16

+

h2

4

= 1 ⇒

h2

4

=

16−6.25

16

⇒ h2 =

9.75×4

16

=

9.75

4

⇒ h2 = 2.44 ⇒ h = √2.44 = 1.56 m approx.