Question

A peacock is sitting on the top of a pillar, which is 9m high. from a point 27 m 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 pounches on it. if their speeds are equal at what distance from the whole is the snake caught?

Answer 1

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Answer 2

Let the hole be at the bottom B of the pole AB

Initially, the snake is at C, so that AC = 27cm

Let v be the common speed of both the snake and the peacock, suppose the peacock catches the snake at point D after time t.

Clearly,

CD = AD = x (say)

In right ∆ABD,we have

AD = x,

AB = 9m

BD = 27-x

By Pythagoras theorem,

$\longrightarrow$$\sf{{AD}^{2}={AB}^{2}+{BD}^{2}}$

$\longrightarrow$$\sf{ {x}^{2} = {9}^{2} + {(27 - x)}^{2}}$

$\longrightarrow$$\sf{ {x}^{2} = 81 + 729 - 54x + {x}^{2}}$

$\longrightarrow$$\sf{54x = 810}$

$\longrightarrow$$\sf{x = 15}$

$\therefore$ $\sf{BD=27-x=27-15=12}$

Hence, the snake is caught at a distance of 12m from the hole.