A hunter tries to hunt a monkey with a small very poisonous arrow, blow form a pipe with initial speed `v_(0)`. The monkey is hanging on a branck of a tree at height `H` above the ground. The hunter is at a distance `L` form the the bottom of the tree. The monkey sees teh arrow leaving the blow pipe and immediately loses the grip on the tree, falling freeely down with zero initial velcoity. The minimum initial speed `v_(0)` of the arrow for hunter to succes while monkey is in air-

Options

A. `sqrt((g(H^(2)+L^(2)))/(2H))`
B. `sqrt((gH^(2))/(H^(2)+L^(2)))`
C. `sqrt((g(H^(2)+L^(2)))/(H))`
D. `sqrt(((2gH^(2)))/(sqrt(H^(2)+L^(2))))`

Answer

A

Explanation

To hit the monkey
`L leR rArr L le (v_(0)^(2)sin 2 theta)/(g) rArr`
`L le (v_(0)^(2)2 sin theta cos theta)/(g)`
`(Lg)/(2sin theta cos theta) le V_(0)^(2) rArr sqrt((Lg)/(2sin theta cos theta)) = V_(0min)`
`sqrt((Lg)/(2xx(H)/(sqrt(H^(2)+L^(2)))xx(L)/sqrt(H^(2)+L^(2))))V_(0(min))`
`rArr sqrt(g(H^(2)+L^(2))/(2H)) =V_(0(min))`