Parabolic Word Problem: An experimental model for a suspension bridge is built....

[kelli]

I have been struggling all week with this one story problem. I saw a post that was similar to this but I kept getting 29 instead of what the answer sheet says which is 18 inches. Please Help!!

An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 9 inches tall and stand 60 inches apart. At some point along the road from the lowest point of the cable, the cable is 1.44 inches above the roadway. Find the distance between that point and the base of the nearest tower.

 

[Deleted member 4993]

I have been struggling all week with this one story problem. I saw a post that was similar to this but I kept getting 29 instead of what the answer sheet says which is 18 inches. Please Help!!

An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 9 inches tall and stand 60 inches apart. At some point along the road from the lowest point of the cable, the cable is 1.44 inches above the roadway. Find the distance between that point and the base of the nearest tower.

I don't see how both the conditions can be true.

 

[Ishuda]

I have been struggling all week with this one story problem. I saw a post that was similar to this but I kept getting 29 instead of what the answer sheet says which is 18 inches. Please Help!!

An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 9 inches tall and stand 60 inches apart. At some point along the road from the lowest point of the cable, the cable is 1.44 inches above the roadway. Find the distance between that point and the base of the nearest tower.

Some assumptions must be made:
-The cables from the tower to the roadway and roadway to tower are in a straight line (or some other given configuration(s) but assume straight line for 'easiest problem').
-The point where the cable touches the roadway is pinned at a given distance from one of the towers (for easiest problem assume point is half way between towers).
-The roadway is level and flat.

Given those 'easiest' assumptions you have two straight lines corresponding to
(1) A line defined by the two points (0,9) and (30,0)
(2) A line defined by the two points (30,0) and (60,9)
Now continue with the rest of the problem and show your work if you get stuck.

If those are not the assumptions to be used, what are they?

EDIT: Oh, and the towers can be represented by a straight vertical line. With those assumptions, I don't get the 18 of the book but I also don't get the 29 you mentioned. By distance between the points you do mean the distance between the (x,1.44) on the left

and (0,0) [(60,0)] don't you?​

 

[stapel]

I have been struggling all week with this one story problem. I saw a post that was similar to this but I kept getting 29...

Please reply showing your work, so we can see what's going on. (Heck, maybe you're right and the answer key is wrong!)

Please be complete. Thank you!