There are 2 poles of length 50m, and a cable 80m long is strung between the poles(assume it is in a parabola shape). The distance from the ground to the lowest point of the cable is 20m. What is the length between the 2 poles?

idk where to start

Guest Mar 30, 2022

#3**+2 **

See diagram below:

given the zeroes, the equation is then

y = (x-0)(x-d)

y = x^2 - dx now sub in the vertex 1/2d, -30

-30 = (1/2d)^2 - d (1/2d)

-30 = 1/4 d^2 - 1/2d^2

-30 = -1/4 d^2

d^2 = 120

d = sqrt (120)

ElectricPavlov Mar 30, 2022

#1**0 **

Unless there's something funny with the cable, it's likely to hang in a catenary rather than a parabola.

Guest Mar 30, 2022

#2**+1 **

The Q said to ASSUME it hangs in a PARABOLIC shape.

I think the distance between the poles is sqrt 120 ..... I'll see if I can work out the solution.....

I am not sure how to include the length of the rope in the solution.....hmmmmm....

ElectricPavlov
Mar 30, 2022

#3**+2 **

Best Answer

See diagram below:

given the zeroes, the equation is then

y = (x-0)(x-d)

y = x^2 - dx now sub in the vertex 1/2d, -30

-30 = (1/2d)^2 - d (1/2d)

-30 = 1/4 d^2 - 1/2d^2

-30 = -1/4 d^2

d^2 = 120

d = sqrt (120)

ElectricPavlov Mar 30, 2022