Question

An arch is in the shape of a parabola whose axis is vertically downwards and measures $80$ mts across its bottom on the ground. Its highest point is $24mts$. The measure of the horizontal beam across its cross section at a height of $18mts$ is

• A. $50$
• B. $40$
• C. $45$
• D. $60$

Answer 1

The correct option is B $40$

Let the equation of the parabola be $x^2=-4ay............\left(1\right)$

It passes through $(40,-24)=>1600=96a$

$=>a=\frac{50}{3}.............\left(3\right)$

Now equation $\left(1\right)$ becomes,

$=>{3x}^2=-200y.................\left(3\right)$

at height of $18m$, ordinate becomes $y=-24+18=-6$

now value of $x$, at $y=-6$ becomes,

$=>{3x}^2=-200(-6)$

$=>x^2=400$

$=>x=\pm 20$

Now cross section at height $18m$ is $=20+20=40m$