Final answer:
To find out how long the ball is in the air, we solve the quadratic equation representing its height over time. The ball is in the air for approximately 3.8 seconds, which is the time we get when we consider the positive value obtained from applying the quadratic formula to the given height equation.
Step-by-step explanation:
To determine how long the ball is in the air using the equation h = -16t^2 + 20t + 4, where h represents the height in feet of the ball at time t seconds after it is thrown, we need to find when the ball hits the ground, which is when h = 0. Solving the quadratic equation -16t^2 + 20t + 4 = 0 using the quadratic formula yields two possible times for when the ball is at height zero: one positive and one negative. Since we cannot have negative time, we take the positive value. Applying the quadratic formula gives us t = 3.79 s and t = 0.54 s. As the ball is at height zero twice during its trajectory, once when it is thrown and once when it lands, we take the longer time to represent how long the ball is in the air, which is approximately 3.8 seconds when rounded to the nearest tenth.