Final answer:
The maximum horizontal distance or range of a ball launched with a horizontal velocity of 10 m/s, taking 0.5 seconds to reach its maximum height, is 10 meters when considering the entire projectile motion duration, including ascent and descent.
Step-by-step explanation:
The student is asking about projectile motion, a topic in physics where an object is launched with an initial horizontal velocity and affected only by the acceleration due to gravity. In this case, the ball is projected with an initial horizontal velocity of 10 m/s, and the time to reach the maximum height is 0.5 seconds.
As there is no acceleration in the horizontal direction (ignoring air resistance), we can calculate the horizontal distance the ball travels by multiplying the initial horizontal velocity by the time it stays in the air until it reaches its maximum height (upwards journey only). The formula to use is:
Horizontal Distance = Horizontal Velocity * Time
Thus, Horizontal Distance = 10 m/s * 0.5 s = 5 meters.
Since the options provided possibly suggest considering the total flight time (including the descent), the horizontal range would then be 10 m/s * (0.5 s * 2) = 10 meters for the entire journey. The choice (C) 10m is the most appropriate for the maximum horizontal distance or range.