Cable car

Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.

Correct result:

y =  62.171 m

Solution:

l=930 m q=67=671000=0.067 y=qx l2=x2+y2 l2=(y/q)2+y2 l2=(1/q2+1)y2  y=l/1+1/q2=930/1+1/0.0672=62.171 ml=930 \ \text{m} \ \\ q=67 ‰=\dfrac{ 67 }{ 1000 }=0.067 \ \\ y=q x \ \\ l^2=x^2 +y^2 \ \\ l^2=(y/q)^2 +y^2 \ \\ l^2=(1/q^2+1)y^2 \ \\ \ \\ y=l / \sqrt{ 1+1/q^2 }=930 / \sqrt{ 1+1/0.067^2 }=62.171 \ \text{m}



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