photography math question.

I want to make sure I have this math right before I start looking at cameras, Also camera suggestions are wecome.

 I am filming an event that will be traveling at about 300 ft per sec. 
 I am fiming about 2 feet of this event.
 My event will last about .006 of a second. 2/300
 If I use a 1200fps camera, I will have about 7.2 frames I can examine. 1200x.006.

I will probably need at least 5 times that many but just checking my math.

2/300 is closer to 0.0067, and you end up with 8 frames instead of 7.2, but yeah.

Presumably you’re planning on capturing hundreds of frames, not just the eight?

As many as I can afford! I have a hunch I will be in the 10,000 fps range which I am not sure if it would be enough.

Is this event repetitive?
If so, it’s much easier to do this with a strobe, and variable delay.
A 10,000 FPS camera is very, very, very pricy.

 We are photographing the action of bow limbs durring a shot. Plenty of slo mo stuff on line where arrows are being photographed. What we are looking for needs to be very precise. We also need to do it with a lot of variables such as added weight on the limb tips and various weight arrows. I found several cameras used in the 4500 fps range which might be fast enough. 

I have a buddy who is a pro who also suggested the strobe, I just didn’t know anything about that.

For this you may also be able to use a conventional still camera and a triggered strobe. You need a mechanism to do the triggering, which could be as simple as a photodector that sees the bowstirng pass though it. You would end up with a single picture with your 8+ frames superimposed upon one another. The bow dynamics would hopefully mean that there are no ambiguous locations, and you should be able to get very high definition and resolution of position.

Yeah, IIRC those pictures of things like a bullet going through an apple or a balloon were done with triggered strobe lights. A strobe that fires for an extremely short duration is a lot cheaper than a fancy camera. For the bullet shots, I recall reading it took fiddling with the timing of the strobe trigger to catch just the right moment.

Set up a bank of 8 strobes to be triggered within 1/10000 of a second of each other and get a superimposed picture of the event.

The trick someone came up with a few years ago was the bank (arc?) of cameras that shot the exact same moment from a sequence of angles, thus allowing the video to apparently pan around a stopped motion. That’s another alternative to consider if you want 3D data.

Knowing the strobe might be preferable is good news. I have a friend who is a cinematographer who actually has all the strobe equipment. I will be using primarily profile shots. We are looking for distorsions in the bow limbs that would account for energy losses and we will be adding variables to see how those distorsions are affected.

There was a TV show called Time Warp that did a bunch of extreme slo-mo stuff. The principal tech guy from that show is with a company called Tech Imaging. No idea on pricing, but they rent out high-speed cameras. They’ve got anything from 1,000 fps to 200,000,000 fps, and they also do studio rentals - it may be cost-effective for you to take your bows there and let their staff worry about the equipment.