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# Real life maths problem - missile slant range watch

1. Okay so I was posting in the News and Current Affairs area about an RAF airstrike on Da'esh. And there's a video of an RAF Tornedo hitting an ISIS vehicle with a Brimstone missile and I wanted to know if there's a scientific/mathematical way to work out the altitude of the aircraft and the distance between the target and the point on the ground below the aircraft when it launched.

I know when the missile is launched (0:41 you can see the heat bloom in the targeting pod's camera that shows it has launched). And the missile hits at 1:05. I know the Brimstone missile travels at 450m/s so that means the slant range (or the hypotenuse) is 10800 meters (24*450)

I also know that the aircraft passes over the target at 1:10 because the targeting pod's camera swivels around, which is what happens when it passes over and now has to look backwards to keep an eye on the target.

Help me maths people; I'm a law student and I can't remember jack about mathematics anymore. Is the hypotenuse/slant range enough to work out the altitude of the aircraft (and therefore the distance between the point on the ground corresponding to the aircraft when it fired the missile and the target point). For argument's sake, let's assume the earth is flat for this problem. Video is below

2. You'd need the angle the hypotenuse makes with the earth.
3. Does the missile definitely travel in a straight line? If so you'd need one more piece of data(there are very many pieces you could use, from the angle that it hits the ground to the horizontal speed of the aircraft to the thrust of the missile and the aerodynamic constants associated with it).
4. The Brimstone is an Active Missile. In other words, once it is launched we have no way of knowing what the internal components of the missile are doing. Hence there is little we can do to determine what is happening in the form of equations because the missile is not ballistic.

However, if you were to get a missile video of a target making determined and at least partially effective evasive manoeuvres then you could draw conclusions about the maximum rate of turn etc.

So far as working out altitude, given the approximate known size of some objects on the ground and knowledge of the planes speed (or some knowledge of the optics of the camera) you might be able to make an estimate of altitude. The assumption of the earth being flat is the least of your errors in this problem.

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Updated: April 26, 2016
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