Cannon `A` is located on a plain a distance `L` from a wall of height `H`. On top of this wall is an idential cannon (cannon B). Ignore air resistance throughout this problem.
Also ignore the size of the cannons relative to `L and H`. The two groups of gunners aim the cannons directly at each other. They fire at each other simultaneously, with equal muzzle speed `v_0`
What is the velue of `v_0` for which the two cannon balls collide just as they hit the ground ?
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Answer

`sqrt((g(L^2 + H^2))/(4 H))`.

Explanation

`v_0 cos ((2 v_0 sin theta)/(g)) + v_0 cos ((2 v_0 sin theta)/(g)) = L`
`sin theta = (H)/(sqrt(H^2 + L^2))`
`cos theta = (L)/(sqrt(H^2 + L^2))`
`v_0^2 = (g L)/(4 sin theta cos theta) rArr v_0 = sqrt((g(L^2 + H^2))/(4 H))`.
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