AC-130 Gunship (Physics of firepower)?

Question

If this simulation was real, what would be the speed of the shells when they hit their target? (meters per second)

http://www.youtube.com/watch?v=NZReuMyPxXM

What would hit the target first, the shells or the sound of the cannon? (make your own estimates)

http://answers.yahoo.com/question/index;_ylt=Aj.J_k7JSRrE0FBumMbSRfzsy6IX?qid=20070723070003AAOojxc


Bonus Question:
Each shell would have the same momentum as a 16 pound bowling ball travelling at what speed on impact?

http://answers.yahoo.com/question/index?qid=20070723065912AAJZBhc&r=w

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http://www.air-attack.com/MIL/ac130/ac130_1_small.jpg
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http://subversatile.net/pics/AC-130-headon-fire-night-med.jpg
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http://www.camo-store.com/images/AC130%20Spectre.jpg
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Answer 1

One of the base definitions of high velocity rounds is that they are faster than the speed of sound. I believe 40mm cannons fire high velocity rounds so the round would hit first. Of course, the plane's sound and earlier firing would reach a target before the rounds aimed at it would so it may not be a surprise to a target when the rounds come pouring in.

As to the 16# bowling ball part, you can, if you can find the values, take the mass of the shells times their speed (initial velocity fed into the standard falling stone formula modified by the effects of air resistance (which leads to "terminal velocity") though at the altitudes I think the planes operate the air resistance might not greatly affect it) squared. This energy will equal the energy of the bowling balls. But momentum is only mass times speed, not speed squared, so divide both sides by the shell velocity to get equal momentums. Once you have the bowling ball's momentum, divide it by the ball's mass to get the speed on impact. For instance, if the shells mass to 1 ounce and their speed is 4,000 ft/sec, then the bowling ball's speed at the same momentum is 250 ft/sec (1 oz * (4,000 ft/sec)^2 * (1 lb/16 oz) = 1,000,000 ft^2-lb/sec^2 and it equals 16 lb * velocity(bowling ball)^2 so (1,000,000 / 16 ft^2/sec^2)^0.5 = velocity of the bowling ball = 62500^0.5 ft/sec = 250 ft/sec).

That's a ball I don't want to set pins for.