A peacock is sitting on the top of a pillar which is9 m high From a point27 m away - Maths - Quadratic Equations

Question

A peacock is sitting on the top of a pillar which is9 m high
From a point27 m away from the bottom of the pillar, a snake is
coming to its hole at the base of the pillar Seeing snake, the
peacock pounces on it If their speeds are equal, at what distance
from hole, the snake caught?

Lalit Mehra · Accepted Answer

Dear Student!

AB is the pillar and C is the position of the hole from the bottom of the pillar Here, AB = 9m and BC = 27 m Let peacock catches the snake at a distance x m from the bottom of the pillar âˆ´ BD = x and CD = 27 â€“ x Given, speed of the peacock and the snake are equal âˆ´ Distance covered by peacock = Distance covered by snake In Î”ABD, AD2 = AB2 + BD2 âˆ´ AD2 = (9)2 + x2 $\Rightarrow AD = \sqrt{81 + x^{2}}$ Distance covered by peacock = $\sqrt{81 + x^{2}} m$ Distance covered by snake = (27 â€“ x) m $∴ \sqrt{81 + x^{2}} = (27 - x)$ Squaring on both sides, we get 81 + x2 = (27 â€“ x)2 âˆ´ 81 + x2 = 729 + x2 â€“ 54x $\Rightarrow 54 x = 729 - 81 = 648 \Rightarrow x = \frac{648}{54} = 12 ∴ 27 - x = 27 - 12 = 15$ Thus, snake is caught at distance 15 m from the hole Cheers!

A peacock is sitting on the top of a pillar which is9 m high. From a point27 m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing snake, the peacock pounces on it. If their speeds are equal, at what distance from hole, the snake caught?