A peacock is sitting on the top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the whole is the snake caught?
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Let AB be the pillar of height 9 meter. The peacock is sitting at point A on the pillar and B is the foot of the pillar. (.. AB = 9)
Let C be the position of the snake which is at 27 meters from B. (.. BC = 27 and ABC = 90)
As the speed of the snake and of the peacock is same they will travel the same distance in the same time...
Now take a point D on BC that is equidistant from A and C. (Please note that snake is moving towards the pillar and hence B-D-C)
Hence by condition 1 AD = DC = y (say)
Take BD = x
Now consider triangle ABD which is a right angled triangle
Using Pythagorus theorem (AB + BD = AD)
.. 9 + x = y
9 = y - x = (y-x)(y+x)
81/(y+x) = (y-x)
y+x = BC = 27
Hence 81/27 = (y-x) = 3
y - x = 3
y + x = 27
Adding gives 2y = 30 or y = 15
x = 27 - y = 12
Thus the snake is caught at a distance of x meters or 12 meters from the hole.