Final answer:
The dolphin spends approximately 1.25 seconds in the air before hitting the water again, which is found by setting the vertical motion model equation h = -16t^2 + 20t + 0 to 0 and solving for t.
Step-by-step explanation:
The question involves the use of the vertical motion model to calculate the time a dolphin spends in the air after jumping out of the water with an initial velocity. The model provided is h = -16t2 + vt + s, where h is the height above the starting point, v is the initial velocity (20 feet per second in this case), t is the time in seconds, and s is the starting height, which is given as 0 feet.
To find the time the dolphin is in the air before it hits the water again, we need to determine when h equals 0 after the initial jump (excluding the starting time). Thus, we solve for t when h is equal to 0:
0 = -16t2 + (20)t + 0
Using the quadratic formula, we determine that the non-zero root of this equation gives the time the dolphin is in the air. After calculation, the root that represents the upward and downward motion of the dolphin is approximately 1.25 seconds.
Thus, the dolphin spends approximately 1.25 seconds in the air before it hits the water again.