Question

A soccer ball is thrown upward from a height of 11 feet with an initial velocity of 20 feet per second. The height of the ball is modeled using the quadratic function h(t) = -16t² + 20t + 11 where h(t) is the height, in feet, of the soccer ball and t is the time the ball has been in the air, in seconds. When is the soccer ball above 15 feet?

Answer 1

The soccer ball is above 15 feet between 0.54 seconds and 3.79 seconds after being thrown upward.

Step-by-step explanation:

To determine when the soccer ball is above 15 feet using the quadratic function h(t) = -16t² + 20t + 11, we would need to solve the inequality h(t) > 15. This would involve finding the values of t for which the function's output is greater than 15. However, the provided information already includes the use of the quadratic formula yielding t = 3.79 seconds and t = 0.54 seconds. Since the question asks for the time intervals when the ball is above 15 feet, we need to determine the start and end times of that interval, which correspond to when the ball is on its way up and when it is coming back down. Therefore, the ball is above 15 feet between 0.54 seconds and 3.79 seconds after it is thrown upward.