Final answer:
The correct horizontal distance that the projectile will travel does not change with mass and the optimal angle for maximal range of a projectile motion is always 45 degrees. Given the answer choices are erroneous concerning these principles, no provided options accurately reflect the physics of projectile motion.
Step-by-step explanation:
Projectile Motion and Optimal Angle for Maximum Range
When a steel projectile weighing 12 grams is shot horizontally at 20.0 m/s from the top of a 49.0 m high tower, we can calculate how far it will travel before hitting the ground. Since there's no horizontal deceleration (ignoring air resistance), you just need to determine the time it takes to fall those 49 meters. Using the formula for an object in free fall, t = √(2h/g), we find the time and then use it to find the distance traveled horizontally, d = vt.
The optimal angle for the maximum distance in projectile motion, regardless of mass, is known as 45 degrees. This is due to the fact that at this angle, the horizontal and vertical components of velocity are equal, maximizing the range.
If the original projectile is replaced with a 20-gram steel projectile, the horizontal distance covered would be the same since mass does not affect the horizontal motion of projectiles (neglecting air resistance).
According to the options given, none of them are correct because the question entails that the mass will not change the horizontal distance covered, but option (a) implicitly suggests that the horizontal distance changes. The angle that achieves the furthest distance is 45 degrees, which isn't an option provided in any of the answer choices. This indicates a possible error in the question or the answer choices.