Question

1.) A highway is to be constructed, passing under the archway of a bridge. The archway is in the form of a half ellipse 30 m wide and 8 m high. Separate lanes, each 3 m wide, are to be built on the highway such that each lane can allow a truck of maximum height of 4 m to pass under the bridge.

How many lanes can be built on the highway?

Answer 1

Answer:

8.66 m

Step-by-step explanation:

Width = 30m = AA'

AC = 30/2 = 15 m

Height = BC = 8 m

Ellipse Equation = (x^2)/ (15^2) + (y^2)/ (8^2) = 1

y = 4m (Truck of this height can pass)

Substitute y = 4 in above equation.

x = (15/2) $\sqrt[]{3}$ = CN

NN' = CN + CN' = 2CN (Since CN=CN') = 15$\sqrt{3}$

Width of each lane = 3m

Number of lanes in NN' = (15$\sqrt{3}$) /3 = 8.66 m