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

A, B

Explanation

`2h = (u_(y)^(2))/(2g)`

or `u_y = 2(sqrt gh)`
Now `(t_2-t_1)u_x = t_2v_x or v_x/u_x = (t_2-t_1)/t_2` ……….(i)
Further `h = u_yt - 1/2 (g t)^2`
or `g t^2 -2u_yt + h = 0`
or `g t^2 - 4(sqrt(gh)) t + 2h = 0`
`t_1 (4sqrt(gh) - sqrt(16gh-8gh))/(2g) = (2-sqrt(2)) (sqrth/g)`
Substituting in Eq. (i) we have,
`v_x/u_x = 2/((sqrt2)+1)` .