A stone is projected from the ground in such a direction so as to hit a bird on the top of a telegraph post of height h and attains the maximum height of 2h above the ground. If at the insatant of projection, the bird were to fly away horizontally with a uniform speed, find the ratio between the horizontal velocity of bird and the horizontal component of velocity of stone, if the stone hits the bird while descending.

Answer

`2/(sqrt(2)+1)`

Explanation

For stone : `2h=((u sin theta)^(2))/(2g)` & `h=(u sin theta)t-1/2 g t^(2)`
`rArr t=(sqrt(40h)+-sqrt(20h))/(10)rArr Deltat=sqrt(0.8h)=2/10 sqrt(20 h)`

Horizontal displacement : `vt_(2)=u cos theta Deltat`
`rArr (v(sqrt(2)+1)sqrt(20h))/10=u cos thetaxx(2sqrt(20h))/10`
`rArr v/(u cos theta)=(2)/(sqrt(2)+1)`