Final answer:
The correct time interval during which the height of the baseball is greater than or equal to 52 feet is for t < 4 seconds.
Step-by-step explanation:
The student is asking about the time interval for which the height of a baseball, represented by h(t)=-1Bt^2 + (B/4)t + 4, is greater than or equal to 52 feet. To solve this, you need to find the value of t when h(t) ≥ 52. This involves solving a quadratic equation. The given information includes a quadratic equation 1² + 1 - 20 = 0 with roots t = -5.0 s and t = 4.0 s. Since negative time doesn't make sense in this context, we consider the positive root t = 4.0 s. The ball's flight duration is divided into an ascent and descent, with the peak height occurring at the midpoint of the flight time.
To do this, we can set the equation equal to 52 and solve for t:
-Bt^2 + B4t + 4 = 52
-Bt^2 + B4t - 48 = 0
Using the quadratic formula, we find that the roots of the equation are t = -5.0 seconds and t = 4.0 seconds.
Thus, the correct answer in this scenario is option b) For t < 4 seconds, because just before reaching 4 seconds, the ball would be at its peak and therefore at or above 52 feet.