Final answer:
The range of a projectile is zero when launched straight up or down at 90° or 0°. The maximum range is achieved at a 45° launch angle. To verify the range at a specific angle and velocity, the projectile motion formula would be used.
Step-by-step explanation:
To determine the range of a projectile, it is important to understand the relationship between launch angle and trajectory. The range is the horizontal distance traveled by a projectile. For a projectile launched on a level surface:
- The range is equal to zero when the projectile is launched either straight up or straight down, which corresponds to angles of 90° (straight up) or 0° (if it's possible to assume a negative projectile motion, straight down).
- The maximum range of a projectile is achieved at a launch angle of 45°, assuming there is no air resistance and the launch and landing heights are the same.
As for the function described as a horizontal line, if f(x) is restricted between x = 0 and x = 20 and is a constant function, its range is simply that single value.
Therefore, for what angle of a projectile is its range equal to zero, the answer is c. 90° (straight up). For the GRASP CHECK regarding the launch angle that maximizes the range of the projectile, the answer is c. 45°. To verify the ranges for projectiles at a 45° launch angle with given initial velocities, you would normally use the range formula for projectile motion, which incorporates velocity, angle, and the acceleration due to gravity.