Final answer:
Considering two identical projectiles fired at different angles with the same initial speed and no air resistance, their speeds at any given elevation will be equal. This is due to the constant effect of gravity on their vertical motion and the unchanged horizontal velocity in the absence of air resistance.
Step-by-step explanation:
When considering two identical projectiles fired with the same initial speed but at different angles and neglecting air resistance, we can derive certain facts about their motion. Given that air resistance is neglected, the only force acting on the projectiles is gravity, which acts downward. This results in a constant downward acceleration for both projectiles, regardless of their horizontal velocity. Thus, when two projectiles reach the same elevation, their vertical velocity components will be the same because they are both influenced by the same gravitational acceleration.
Their horizontal motion, however, remains unaffected by gravity. Since they were projected with the same initial speed and there are no forces acting horizontally (assuming no air resistance), their horizontal velocities also remain constant and equal. Therefore, at any given elevation, the speed of projectile A will be the same as the speed of projectile B.