Final answer:
The projectile's horizontal speed after falling 25 meters remains the same as its initial horizontal speed, 35 meters per second since there is no horizontal acceleration in projectile motion when neglecting friction.
Step-by-step explanation:
In the context of projectile motion, the initial horizontal speed of a projectile launched horizontally from a height will remain constant if we neglect air resistance (friction). The student's question involves a projectile launched with an initial horizontal speed of 35 meters per second from a height of 65 meters. Since there is no horizontal acceleration due to gravity, and we are neglecting friction, the projectile's horizontal speed will remain at 35 meters per second regardless of how far it has fallen vertically. There is no horizontal force applied to the projectile in mid-air; thus, its horizontal velocity component does not change.