[Physics] Two cannons are fired from a boat, boat A is closer and boat B further. Which gets hit first

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A battleship (X) simultaneously fires two cannons towards two enemy ships. One close by (A) and one far away (B). The canon leave the battleship at different angles and travel along trajectories. Which boat gets hit first?

Answer: Boat B because the cannon doesn't need to go as high as it needs for boat B as it will take longer to travel way up than back down.

The distance on water between X and A is less compared to X and B. The cannons make this rainbow-like curved line as it travels to both boats (the line objects make when you throw them upwards). The top of the curve (when tangent is horizontal) for A is higher than B. So wouldn't the cannon still take more time to travel from X to B than X to A? Because if its tangent is lower in the air than A, its distance between X and B is still more than X and A.

How is the answer BOAT B?

Best Answer

If you have a cannon that shoots a ball at a constant velocity, there are two solutions that allow you to hit a target at a given distance. (Mathematically, the solution is a quadratic with two roots.)

As an extreme example, if your target is 100 feet away, you can hit it by shooting directly at it, (with an almost insignificant ballistic arc), or you can hit it by shooting almost straight up, sending the ball thousands of feet into the air and having it fall back down 100 feet away. So in your example, if you take the 'direct fire' path to the far target, and the 'parabolic' path to the near target, you can indeed hit the far target first.

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