A peacock on a pillar of $9$ feet height on seeing a snake coming towards its hole situated just below the pillar from a distance of $27$ feet away from the pillar will fly to catch it. If both possess the same speed, how far from the pillar they are going to meet?

Open in App

Solution

Let the peacock and snake meet at $x$ m from the pillar as shown in the above figure:

Let $B D = x$ . It is given that the peacock is on a pillar of $9$ feet height, therefore, $A B = 9$ and the given distance is $27$ feet from the pillar, therefore, $A D = (27 - x)$

In $△ A B D$ , using pythagoras theorem, we have

$A D^{2} = A B^{2} + B D^{2} \Rightarrow (27 - x)^{2} = 9^{2} + x^{2} \Rightarrow 27^{2} + x^{2} - (2 \times 27 \times x) = 81 + x^{2} (∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b) \Rightarrow 729 + x^{2} - 54 x = 81 + x^{2} \Rightarrow 729 + x^{2} - 54 x - 81 - x^{2} = 0 \Rightarrow 54 x - 648 = 0 \Rightarrow 54 x = 648 \Rightarrow x = \frac{648}{54} \Rightarrow x = 12$

Hence, the peacock and snake are going to meet at a distance of $12$ feet from the pillar.

Suggest Corrections

Similar questions

Q. A peacock is sitting on the top of a pillar, which is

9 m

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 pounces on it. If their speeds are equal, at what distance from the whole is the snake caught?

The angle of elevation of the top of a pillar at any point $A$ on the ground is $15^{\circ}$ . On walking $100$ ft. towards the pillar, the angle becomes $30^{\circ}$ . Height of the pillar and its distance from $A$ are _______ and _______ respectively.

Q. A flagstaff stands vertically on a pillar,the height of the flagstaff being double the height of the pillar. A man on the ground at a distance finds that both the pillar and the flagstaff subtend equal angles at his eyes. The ratio of the height of the pillar and the distance of the man from pillar, is

Two pillars of equal heights stand on either side of a road which is 100 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are $60^{\circ}$ and $30^{\circ}$ . Find the height of each pillar and position of the point on the road.

Q. A person wants to see two pillars from a distance of 11 km, separately. The distance between the pillars must be approximately

Join BYJU'S Learning Program

A peacock on a pillar of 9 feet height on seeing a snake coming towards its hole situated just below the pillar from a distance of 27 feet away from the pillar will fly to catch it. If both possess the same speed, how far from the pillar they are going to meet?

A peacock on a pillar of $9$ feet height on seeing a snake coming towards its hole situated just below the pillar from a distance of $27$ feet away from the pillar will fly to catch it. If both possess the same speed, how far from the pillar they are going to meet?