Canon A is located on a plain a distance L from a wall of height H. On top of this wall is an identical 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 v0. What is the value of v0 for which the two cannon balls collide just as they hit the ground?
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a
12gL2+H2H
b
gL2+H2H
c
2gL2+H2H
d
gL2+H22H
answer is A.
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Detailed Solution
v0cosθ2v0sinθg+v0cosθ2v0sinθg=Lsinθ=HH2+L2 and cosθ=LH2+L2v02=gL4sinθcosθ⇒ v0=gL2+H24H=12gL2+H2H