Question

A bridge has a parabolic arch that is 10 m high in the centre and 30 m wide at the bottom. Find the height of the arch 6m from the centre, on either sides

Answer 1

PQ = 2a = 30 m

a = 15 m

Point Q be (15 , –10)

Equation of the parabola

x² = – 4 ay  .......(1)

Q lies on parabola

15² = – 4a( –10)

a = `225/40`

(1) ⇒ x² = `- 4(225/40)y`

x² = `225/10 y`

Let B(6, y) lies on parabola

6² = `225/10 y_1`

y₁ = `- (36 xx 10)225`

= `(- 8)5`

= `8/5 "m"`

AB = AC – BC

= `10 - 8/5`

= `(50 - 8)/5`

= `42/5`

AB = 8.4 m

∴ The height of the arch 6 m from the centre is 8.4 m