Final answer:
To determine the time it takes for the ball to hit the ground, set the height equation to zero and solve for t using the quadratic formula. The correct solution for t is 4.0 seconds, as time cannot be negative.
Step-by-step explanation:
To find out how long it took for the ball to hit the ground after being kicked from a balcony 201 feet above the ground, we need to solve the equation h(t) = 20 - 16t² for when h(t) is equal to 0, which represents the height of the ground level. Setting the equation 0 = 20 - 16t² equal to zero and solving for t gives us a quadratic equation.
Using the quadratic formula, we have two potential solutions for t: t = -5.0 s and t = 4.0 s. Since time cannot be negative in this context, we disregard t = -5.0 s and consider t = 4.0 s as the correct answer. The ball takes 4.0 seconds to hit the ground after being kicked from the balcony.
It's worth noting that the equation provided, h(t) = 20 - 16t², does not seem to match the initial scenario of the ball being kicked from a height of 201 feet, but it's important to solve the task as described.