Final answer:
Cannons A and B will have the same horizontal range when fired at angles of 25 degrees and 65 degrees respectively, as the sum of their launch angles equals 90 degrees, which gives identical ranges for the same initial speed.
Step-by-step explanation:
When cannons A and B fire under identical conditions, except for their launch angles—with cannon A at 25 degrees and cannon B at 65 degrees—their horizontal ranges will be the same. According to projectile motion principles, for any given initial speed, there are two launch angles that yield the same range when their sum equals 90 degrees. Assuming there is no air resistance, this phenomenon occurs because both the vertical velocity components will be equal in magnitude but of opposite signs at the time of launch, resulting in the projectiles spending the same amount of time in the air.
Therefore, even though cannon A fires at a lower angle to the horizontal and cannon B fires at a steeper angle, both will cover the same horizontal range if their launch angles add up to 90 degrees, which in this case they do (25 degrees + 65 degrees = 90 degrees). However, the trajectory heights will differ, with the shot at 65 degrees reaching a higher apex than the one at 25 degrees.