Question

The towers of a bridge hung in the form of a parabola ;have their tops 30m above the road way and are 200 m apart if the cable is 5m above the roadway

Answer 1

Refer to the attachment.

${ \color{red}\odot} \rm \:Question$

The towers of a bridge hung in the form of a parabola ; have their tops 30 m above the road way and are 200 m apart. If the cable is 5m above the roadway.

$\color{blue}{ \ast} \bf \: Answer$

$\red{ \boxed{ \begin{array}{c} \frac{29}{4} \end{array} }} \: \star$

Solution

A and B are the top of the towers. AE and BF are the height of the towers. H is the center of the bridge. HI is the 5 m above from the roadway.

Here, the equation of the parabola will be

$\color{blue}\ast \: \rm \boxed {{x}^{2} = 4ay}$

From figure ( Top of Tower )

• x-cordinate is 100 m
• y-coordinate is 25 m .

On Implementation ,

$: \implies \sf100 ^{2} = 4a(25) \\ : \implies \boxed{a = 100}$

Again, length of the vertical supporting cable,

30 m from the center is y + 5.

Find

• Ordinate ( y coordinate )

$: \implies \rm 900 = 4(100)y$

Since, x ordinate = 30

$: \implies \rm \:y = \frac{900}{400}$

$\therefore \bf \: y = \dfrac{9}{4}$

Vertical Length = y + 5 , use the value for y

$: \implies {\underline{\boxed{\rm{ \frac{9}{4} + 5 = \frac{29}{4} }}}} \: \ast$

Conclusion

Therefore, the vertical length of cable is

$\color{red}{ \rm\frac{29}{4} m}$

Thankyou

Answer 2

Answer:

A and B are the top of the towers. AE and BF are the height of the towers. H is the center of the bridge. HI is the 5 m above from the roadway.

Here, the equation of the parabola will be: x2 = 4ay

From figure, x-cordinate of top of tower is 100 m and y-coordinate is 25 m.

(1)=> 1002 = 4a(25)

or a = 100

Again, length of the vertical supporting cable, 30 m from the center is y + 5.

Find y co-ordinate

(1)=> 900 = 4(100)y [x-coordinate of the point is 30]

or y = 9/4 Vertical length = y + 5 = 9/4 + 5 = 29/4

Therefore, the vertical length of cable is 29/4 m