Question

john hits a fly ball into the air. the ball reaches a maximum height of 200 ft after 4 seconds. what is a reasonable domain of the fly ball? all real numbers between 0 seconds and 4 seconds; all real numbers between 0 feet and 200 feet; all real numbers between 0 feet and 400 feet; all real numbers between 0 seconds and 8 seconds

Explanation:

Step1: Define domain context

The domain of a function describing the ball's height refers to the valid time values during which the ball is in the air.

Step2: Analyze flight symmetry

The ball reaches maximum height at 4 seconds. Projectile motion (ignoring air resistance) is symmetric, so the time to rise equals the time to fall.

Step3: Calculate total flight time

Total time = time up + time down = $4 + 4 = 8$ seconds. The ball starts at $t=0$ and lands at $t=8$.

Answer:

All real numbers between 0 seconds and 8 seconds