Question

How do I calculate this? Is there a formula?

Answer 1

Answer:

Height of cables = 23.75 meters

Step-by-step explanation:

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of $x = 600$ or $x = -600$, and y at 95.

We know that the equation of a parabola is in the form $y=ax^2$ and here it passes through the point $(600, 95)$.

$y=ax^2$

$95=a \times 600^2$

$a=\frac{95}{360000}$

$a=\frac{19}{72000}$

So new equation for parabola would be $y=\frac{19x^2}{72000}$.

Now we have to find the height $(y)$of the cable when $x= 300$.

$y=\frac{19 (300)^2}{72000}$

y = 23.75 meters

Answer 2

Answer: 23.75 meters

Step-by-step explanation:

If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:

$y = a (x-0) ^ 2 + 0\\\\y = ax ^ 2$

We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.

Thus:

$95 = a (600) ^ 2$

$a = \frac{95} {600 ^ 2}\\\\a = \frac {19} {72000}$

Then the equation is:

$y = \frac{19}{72000} x ^ 2$

Finally the height of the cables at a point 300 meters from the center is:

$y = \frac{19}{72000}(300) ^ 2$

$y =23.75\ meters$