Johnny has recently constructed a cannon, and he wants to a hit a ground target that is **distance** units away. The cannon shoots bullets at **velocity** units per second. When a bullet is in the air, its flight follows the standard laws of physics. This means that if he shoots a bullet at angle *alpha* from the ground, it will travel a distance of
( 2 * **velocity**^2 * sin(*alpha*) * cos(*alpha*) ) / *g* ,
where *g* is the acceleration of gravity on Earth. In this problem, we will use 10 as the value of *g*.
The cannon can only be set at the angles given in the int[] **angles** (all angles are given in degrees). Johnny must pick the angle that will land the bullet as close as possible to the target. Return this closest possible distance between the landing point and the target as a double. |