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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let PQ be the pole and the peacock is sitting at the top P of the pole. Let the hole be at Q. Initially, the snake is at S when the peacock notices the snake such that QS=27m

Suppose v m/sec is the common speed of both the snake and the peacock and the peacock catches the snake after t seconds at point T. clearly distance travelled by the snake in t seconds is same as the distance flown by peacock

∴PT=ST=x

Thus, in right triangle PQT, we have

QT=27−x,PT=x and PQ=9

Using Pythagoras theorem, we have

PT^  2  =PQ^2  +QT^  2  ⇒x^  2  =9^  2  +(27−x)^  2

 

⇒x  ^2  =81+729−54x+x  2  ⇒0=810−54x⇒54x=810⇒x=15

∴QT=SQ−ST=(27−15)m=12m

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