Final answer:
To find the time it takes for the ball to reach a height of 64 feet, we can set the equation h(t) = 64 and solve for t using the quadratic formula. The two solutions are t = 0.54 seconds and t = 3.79 seconds. Since we are looking for the longer time, the ball will take approximately 3.79 seconds to reach a height of 64 feet in the air.
Step-by-step explanation:
To find the time it takes for the ball to reach a height of 64 feet, we need to set the equation h(t) = 64 and solve for t.
The equation given is h(t) = -16t^2 + 64t, where h is the height of the ball in feet and t is the time in seconds.
Plugging in 64 for h, we get 64 = -16t^2 + 64t.
This is a quadratic equation which we can solve using the quadratic formula.
Using the quadratic formula, we find that the two solutions are t = 0.54 seconds and t = 3.79 seconds.
Since we are looking for the time it takes for the ball to reach a height of 64 feet, we take the longer solution, which is t = 3.79 seconds.
Therefore, it will take the ball approximately 3.79 seconds to reach a height of 64 feet in the air.