I know you like maths..

iamdjdz

iamdjdz

iamdjdz

Soldato
Joined
24 Nov 2006
Posts
5,049
Just been given this problem by my brother:

x43x1u.jpg


Missing words on the right are:
The other
Taught wire
Intersect

Anyone got any idea?

My answer is cos(h) but don't know if that's right?
 
I think the intersection point is 2/3 h (two thirds of h). That's my stab anyway.

Calculated by writing down the linear equations of each wire and solving for the intersection point where y in both equations would be equal.
 
yes the awnser is 2/3h, you can use simultaneous linear equations to solve this but thats the long way of doing things, much easier approach is to just use ratio rules of intersecting points of parallel lines to figure this out. Its very early in the morning and my mind is not 100% alert but here goes, I have deliberately prvoided more working out than is necessary for understanding of explanation.

Please refer to diagram for labelling of points.

eQRZM2C

http://imgur.com/eQRZM2C
eQRZM2C


Assume, AB, GH, ZY are parallel lines ( if this assumption is not made then it makes things a little more tricky, for your application and level of question I think its the most logical assumption to be made)

the ratio of lines AB : ZY = AG : YG
but AB = h and ZY = 2h this implies the ratio AG : YG = h : 2h ie 1 : 2
so we have AG : YG = 1: 2, further more we know that the line segment AY = b ( lenght of b, whatever b is does not matter here)
but we also know this line segment is split into the ratio of 1:2 ( AG:YG) so this implies AG = (1/3)b and YG = (2/3)b

We also know that AG : YG = AH : ZH this implies AG = (1/3)b : YG = (2/3)b = AH : ZH. We also know that AZ = c, this imples that the
line segment AZ of length c is split in the ratio 1:2. Meaning that AH = (1/3)c and ZH = (2/3)c.

now we also know that the ratio of

GH : ZY = AH : AZ BUT we know that GH = x and ZY = 2h and AH = (1/3)c and AZ = c. Using these values in GH : ZY = AH : ZH we get

x : 2h = (1/3)c : c and rewriting the ratios as quotients we get

(x/2h) = (1/3)c / c

(x/2h) = (1/3) / (1) [ the c cancell out here]
rearrange to give

x = 2h * [(1/3) / (1)]

x = (2/3) h

I hope its all correct, its too early in the morning for this :D
 
Last edited:
First step is to work out that the point of intersection is 1/3 of the horizontal distance from the short post to the second post. Then it's just similar triangles.
 
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