question_answer

If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is   JEE Main Online Paper (Held On 07 May 2012)

A) 16           

B)                        18

C)                        50                                          

D)                        15

Correct Answer: A

Solution :

We put one pole at origin. \[BC=80m,OA=20m\] Line OC and AB intersect at M. To find: Length of MN. Eqn of OC:\[y=\left( \frac{80-0}{a-0} \right)x\]\[\Rightarrow \]\[y=\frac{80}{a}x\]?.(1) Eqn of AB: \[y=\left( \frac{20-0}{0-a} \right)\left( x-a \right)\] \[\Rightarrow \]\[y=\frac{-20}{a}\left( x-a \right)\]                                          ?(2) AtM: (1)=(2) \[\Rightarrow \]\[\frac{80}{a}x=\frac{-20}{a}\left( x-a \right)\]\[\Rightarrow \]\[\frac{80}{a}x=\frac{-20}{a}x+20\] \[\Rightarrow \]\[x=\frac{a}{5}\]\[\therefore \]\[y=\frac{80}{a}\times \frac{a}{5}=16\]