# Game of Drones - Zap it!

Your programmable drone is pitted against another drone in a rectangular 3D arena measuring 40 meters long, 40 meters wide and 20 meters high. You have equipped your drone with a laser gun that will take your opponent down as soon as it is within 1 meter reach. This laser makes your drone slightly slower (9.70 m/s maximum speed) compared to your opponent's drone which lacks any weapons and which can reach 10.00 m/s. Both drones are equipped with cameras and accurate accelerometers. All this information is available to on-board processors which control the drone movements and which for all practical purposes can be assumed to be fast enough to avoid any measurable latency in the drone's responses to new information. Apart from the laser action, neither drone can influence the movements of the other (air currents and other aerodynamic interactions can be assumed to be insignificant), and both drones are light enough for gravity to be negligible.

Your opponent is allowed to select a starting corner, and your drone is placed in the opposing corner, and subsequently both drones are released at the same time. To make things a bit more challenging for you, prior to the drone battle your opponent is allowed a detailed inspection of the program that controls the movements of your drone.

Can you device a strategy that guarantees your drone takes down the opponent's drone?

• Wouldn't always flying directly towards your target work? You'd get within a meter eventually. Jan 20, 2015 at 17:52
• If the target moves in a circle and the attack drone always aims directly at it, it would not be able to catch up because it is slower. Jan 20, 2015 at 18:02
• @FlorianF How big of a circle and how far behind do you need to be? You don't have to catch it, just get within a metre. Jan 20, 2015 at 18:04
• It looks a radius of 5 would be large enough. You need sqrt(radius^2-(radius*.97)^2)>1 in the long term. This is for a stupid drone who aims straight at the target. Jan 20, 2015 at 22:51
• @FlorianF: That's only accurate if you aim directly where the defending drone was. If you aim for where the defending drone is, then the "radius" of your circle is smaller. However, if his circle is big enough, the radius difference may not be enough to catch up, I'd have to do the math. Jan 20, 2015 at 23:54

The attack drone should fly to a virtual target that is always at 29/30 of the way from the center of the room to the target drone. That point moves 3.3% slower than the target drone.

Since the attack drone flies only 3% slower than the target drone, it can reach that virtual target in a finite time regardless how the target drone moves.

Since the maximum distance from the center to any place of the room is a convenient 30 meters, the distance between the virtual target and the real target is never more than 1 meter. So when the attack drone reaches the virtual target, the real target is in range.

And Zap!

• I like it! Short, crisp, and obvious. Well done! Jan 20, 2015 at 17:58

You drone should just takeoff and then shoot immediately.

The person who sold you a "1 meter reach" laser clearly doesn't understand how light works.

• Didn't downvote, but you can equally view the drone as using a lightsaber or something instead. Unless the question is asking for you to intentionally think outside the box, or there is in fact no good answer, there is no need to provide such answers. Jan 21, 2015 at 10:04
• Lasers diffuse with distance and interactions with the atmosphere. It could be that the laser is only optimally functional within 1 metre and that outside that range it diffuses too much to be effective. Jan 21, 2015 at 13:21
• The "laser" is one of these translucent tubes with leds inside that you find in toy shops. I am pretty sure you can down a drone with that. Jan 21, 2015 at 16:37