Two cannons are pointed directly towards each other, (one on theground pointing

Question

Two cannons are pointed directly towards each other, (one on theground pointing upwards, A, second on a hill pointing downwards, B.both pointing at each other). When fired, the cannonballs willfollow the trajectories, crossing each others path, in an archedmanner. If we want cannonballs to hit each other, should the guncrews fire cannon A first, cannon B first, or should they firesimultaneously? ignore any effects due to air resistance.

Explanation / Answer

Let us assume the height of the hill to be H , horizontaldistance between them D , and A makes an angle withthe ground. Let velocity of projection be V. Let they be fired simultaneously and time be t secs. if they meet , Vsin T + .5gt2 +Vsin T- .5gt2 =H So 2 Vsin T   =H .........1 also Vcos T   +Vcos T =D =>2Vcos T=D............2 these equations have a solution for properly chosen V,. So they must be fired simultaneously.

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