InterviewSolution
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InterviewSolution
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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.A. `2/(sqrt2+1)`B. `1/(sqrt2+1)`C. `2/(sqrt2-1)`D. `1/(sqrt2-1)` |
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Answer» Correct Answer - A Let the stone is projected with a velocity `u` at an angle `theta` with the horizontal, we have `(2h)=((u sin theta)^(2))/(2g) or u sin theta=2sqrtgh` Suppose `t` is the time taken by the stone to reach the height `h` above the ground.Then `h=u sin theta t-1/2g t^(2) or (g t^(2))/2-u sin thetat+h=0` As we have `u sin theta =2sqrt(gh)` `:. (g t)^(2)/2-2sqrt(gh)t+h=0` Solving above equation for `t`, we get `t=(2sqrt(gh)+-sqrt((2sqrt(gh))^(2)-4xxg/hh))/(2xxg/2)&t_(2)sqrt((2h)/g)(sqrt2+1)` Where `t_(1)` and `t_(2)` correspond to `P` and `Q` in the figure.Suppose `v` is the horizontal velocity of the bird. Then `PQ=vt_(2)`. |
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