Answer

Verified

426.6k+ views

**Hint:**In this question we will try to make a figure according to the given information and determine the points on parabola at height $18\,m$ where the cross section of beam measures .Then we will write the equation of the parabola. And with the help of equations we will find the answer.

**Complete step-by-step answer:**

Let equation of the given vertically downward parabola be ${x^2} = - 4ay\,\,\,\,\,\,\,\,\,\,\,\,\, \to (1)$

Given the measure of bottom on ground is $80\,m$

And the highest point is $24\,m$

So we can clearly now find the points A and B‘s coordinates.

$A \equiv ( - 40, - 24)\,\,\,\,\& \,\,\,B \equiv (40, - 24)$

And both of these points lie on parabola so A must satisfy (1)

$

{(40)^2} = - 4a( - 24) \\

1600 = 96a \\

a = \dfrac{{50}}{3}\,\,\,\,\,\,\,\,\,\,\, \to (2) \\

$

Now putting this value in (1)

$

{x^2} = - 4\left( {\dfrac{{50}}{3}} \right)y \\

3{x^2} = - 200y\,\,\,\,\,\,\,\, \to (3) \\

$

Now we need to find the value of $x$ at $y = - 6$ by putting it in (3)

$

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

3{x^2} = 1200 \\

{x^2} = 400 \\

x = \pm 20 \\

$

Now coordinates of C becomes $( - 20, - 6)$ and D becomes $(20, - 6)$.

Now distance between C and D is,

$

CD = \sqrt {{{(20 - ( - 20))}^2} + {{( - 6 - ( - 6))}^2}} \\

CD = \sqrt {{{40}^2} + {0^2}} \\

CD = 40 \\

$

So the horizontal beam across its cross section at a height of $18\,m$ is of measure $40\,m$.

**So, the correct answer is “Option B”.**

**Note:**The tricky part in the question is that we need to find the measure of height of the horizontal beam across its cross section at a height of $18\,m$. Generally we take $18\,m$ as the ordinate but actually by seeing the figure we can clearly see that $18\,m$ is not ordinate and we need to subtract $24\,m$ from it.

Recently Updated Pages

Which of the following is correct regarding the Indian class 10 social science CBSE

Who was the first sultan of delhi to issue regular class 10 social science CBSE

The Nagarjuna Sagar project was constructed on the class 10 social science CBSE

Which one of the following countries is the largest class 10 social science CBSE

What is Biosphere class 10 social science CBSE

Read the following statement and choose the best possible class 10 social science CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Why is the Earth called a unique planet class 6 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

One cusec is equal to how many liters class 8 maths CBSE