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Q.

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

v0cos⁡θ2v0sin⁡θg+v0cos⁡θ2v0sin⁡θg=Lsin⁡θ=HH2+L2 and cos⁡θ=LH2+L2v02=gL4sin⁡θcos⁡θ⇒ v0=gL2+H24H=12gL2+H2H
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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?