Question

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. Find its width at a distance of 2m from its vertex. (class 11)​

Answer 1

hiiii ayush

See ayush

, axis is vertical , so let arc of parabola is in the form of x² = 4ay

here, OB = 10 m

AC = 5 m so, AB = BC = 5/2 = 2.5 m

so, the co-ordinate of A = ( 2.5 , 10)

point A ( 2.5, 10) will satisfy equation of parabola .

so,

( 2.5)² = 4 × a × 10

6.25 = 40a

a = 6.25/40 = 5/32

now, equation of parabola is x² = 4 × 5/32y

x² = 5y/8 __________(1)

Let OR = 2 m and PQ = k then, RP = k/2

hence, point P( k/2, 2) .

point P will also satisfy equation of parabola .

put P ( k/2, 2) in equation (1)

(k/2)² = 5 × 2/8

k²/4 = 5/4

k = ±√5 but k is distance so, K won't be negative.

k = √5 .

hence, √5 m wide it is 2m from the vertex of the parabola.

hope it will help u

Answer 2

Step-by-step explanation:

See the attachment .....