Question

a peacock is sitting on the top of a pillar 18m high. From a point 54m away from the bottom of the pillar,a snake is coming to its hole at the bottom 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,pls answer correctly and give full solution,i will mark u the brainliest​

Answer 1

Answer:

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