Final answer:
Using the equations of projectile motion, the projectile lands at a distance determined by the time it falls under gravity and its initial horizontal speed. The optimal angle for the furthest distance is 45°, and changing the projectile's mass won't affect the distance landed if air resistance is ignored.
Step-by-step explanation:
To determine how far from the base of a 49.0 m high tower a 12 gram steel projectile shot horizontally at 20.0 m/s will land, we use the formulas of projectile motion. We first calculate the time it takes for the projectile to hit the ground due to gravity using the equation for vertical motion d = ½gt², where d is the vertical distance, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds. Once we have the time, we can find out how far the projectile travels horizontally by using the equation horizontal distance = horizontal velocity × time.
To reach the furthest distance, the ideal launch angle above the horizontal is 45°. This angle provides the maximum range for projectile motion when air resistance is negligible. Prime considerations like air resistance and elevation change can affect practical applications, but the physics theory reveals the 45° angle as a general principle for max range.
In the case of replacing the original projectile with a heavier 20-gram projectile, as long as we are ignoring air resistance and the projectile is shot with the same initial speed and angle, the distance from the base of the tower will remain the same. This is because, in a vacuum, all objects fall at the same rate regardless of their mass.